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If the roots of a quadratic equation ax2 + bx + c = 0 are α and β, then the quadratic equation having roots α2 and β2 is
- a)x2 – (b2 – 2ac) x + c = 0
- b)a2x2 – (b2 – 2ac) x + c = 0
- c)ax2 – (b2 – 2ac) x + c2 = 0
- d)a2x2 – (b2 – 2ac) x + c2 = 0
Correct answer is option 'D'. Can you explain this answer?
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If the roots of a quadratic equation ax2 + bx + c = 0 are α and &...
Answer:
To find the quadratic equation with roots 2 and 2, we can use the fact that the sum and product of the roots of a quadratic equation can be expressed in terms of the coefficients of the equation.
Let's denote the roots as α and β. The sum of the roots is given by α + β = -b/a, and the product of the roots is given by αβ = c/a.
Given that the roots are 2 and 2, we can substitute these values into the sum and product formulas:
α + β = 2 + 2 = 4
αβ = 2 * 2 = 4
Now, let's find the quadratic equation using these values.
Step 1: Finding the sum and product of the roots
From the given quadratic equation ax^2 + bx + c = 0, we have the sum of the roots:
α + β = -b/a
Substituting the values α + β = 4 and αβ = 4, we can solve for b/a:
4 = -b/a
Step 2: Expressing the quadratic equation in terms of the sum and product of the roots
We can express the quadratic equation using the sum and product of the roots as follows:
x^2 - (α + β)x + αβ = 0
x^2 - 4x + 4 = 0
Step 3: Simplifying the equation
To simplify the equation further, we can divide it by a to obtain the final quadratic equation:
(a^-1)x^2 - (4/a)x + 4/a = 0
Since a^-1 is equivalent to a^2, we can rewrite the equation as:
a^2x^2 - (4/a)x + 4/a = 0
Comparing this equation with the given options, we find that the correct answer is option D:
a^2x^2 + (b^2 - 2ac)x + c^2 = 0
where a^2 = a, b^2 - 2ac = -4/a, and c^2 = 4/a.
To find the quadratic equation with roots 2 and 2, we can use the fact that the sum and product of the roots of a quadratic equation can be expressed in terms of the coefficients of the equation.
Let's denote the roots as α and β. The sum of the roots is given by α + β = -b/a, and the product of the roots is given by αβ = c/a.
Given that the roots are 2 and 2, we can substitute these values into the sum and product formulas:
α + β = 2 + 2 = 4
αβ = 2 * 2 = 4
Now, let's find the quadratic equation using these values.
Step 1: Finding the sum and product of the roots
From the given quadratic equation ax^2 + bx + c = 0, we have the sum of the roots:
α + β = -b/a
Substituting the values α + β = 4 and αβ = 4, we can solve for b/a:
4 = -b/a
Step 2: Expressing the quadratic equation in terms of the sum and product of the roots
We can express the quadratic equation using the sum and product of the roots as follows:
x^2 - (α + β)x + αβ = 0
x^2 - 4x + 4 = 0
Step 3: Simplifying the equation
To simplify the equation further, we can divide it by a to obtain the final quadratic equation:
(a^-1)x^2 - (4/a)x + 4/a = 0
Since a^-1 is equivalent to a^2, we can rewrite the equation as:
a^2x^2 - (4/a)x + 4/a = 0
Comparing this equation with the given options, we find that the correct answer is option D:
a^2x^2 + (b^2 - 2ac)x + c^2 = 0
where a^2 = a, b^2 - 2ac = -4/a, and c^2 = 4/a.
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If the roots of a quadratic equation ax2 + bx + c = 0 are α and β, then the quadratic equation having roots α2 and β2 isa)x2 – (b2 – 2ac) x + c = 0b)a2x2 – (b2 – 2ac) x + c = 0c)ax2 – (b2 – 2ac) x + c2 = 0d)a2x2 – (b2 – 2ac) x + c2 = 0Correct answer is option 'D'. Can you explain this answer?
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If the roots of a quadratic equation ax2 + bx + c = 0 are α and β, then the quadratic equation having roots α2 and β2 isa)x2 – (b2 – 2ac) x + c = 0b)a2x2 – (b2 – 2ac) x + c = 0c)ax2 – (b2 – 2ac) x + c2 = 0d)a2x2 – (b2 – 2ac) x + c2 = 0Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If the roots of a quadratic equation ax2 + bx + c = 0 are α and β, then the quadratic equation having roots α2 and β2 isa)x2 – (b2 – 2ac) x + c = 0b)a2x2 – (b2 – 2ac) x + c = 0c)ax2 – (b2 – 2ac) x + c2 = 0d)a2x2 – (b2 – 2ac) x + c2 = 0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of a quadratic equation ax2 + bx + c = 0 are α and β, then the quadratic equation having roots α2 and β2 isa)x2 – (b2 – 2ac) x + c = 0b)a2x2 – (b2 – 2ac) x + c = 0c)ax2 – (b2 – 2ac) x + c2 = 0d)a2x2 – (b2 – 2ac) x + c2 = 0Correct answer is option 'D'. Can you explain this answer?.
If the roots of a quadratic equation ax2 + bx + c = 0 are α and β, then the quadratic equation having roots α2 and β2 isa)x2 – (b2 – 2ac) x + c = 0b)a2x2 – (b2 – 2ac) x + c = 0c)ax2 – (b2 – 2ac) x + c2 = 0d)a2x2 – (b2 – 2ac) x + c2 = 0Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If the roots of a quadratic equation ax2 + bx + c = 0 are α and β, then the quadratic equation having roots α2 and β2 isa)x2 – (b2 – 2ac) x + c = 0b)a2x2 – (b2 – 2ac) x + c = 0c)ax2 – (b2 – 2ac) x + c2 = 0d)a2x2 – (b2 – 2ac) x + c2 = 0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of a quadratic equation ax2 + bx + c = 0 are α and β, then the quadratic equation having roots α2 and β2 isa)x2 – (b2 – 2ac) x + c = 0b)a2x2 – (b2 – 2ac) x + c = 0c)ax2 – (b2 – 2ac) x + c2 = 0d)a2x2 – (b2 – 2ac) x + c2 = 0Correct answer is option 'D'. Can you explain this answer?.
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