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If alpha and beta are the roots of 4x square plus 7xplus 2=0 then the equation whose roots are alpha square and beta square is?
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If alpha and beta are the roots of 4x square plus 7xplus 2=0 then the ...
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If alpha and beta are the roots of 4x square plus 7xplus 2=0 then the ...
Given Problem:
4x^2 + 7x + 2 = 0
Finding Roots:
Using the quadratic formula, we can find the roots of the given equation as alpha and beta.
Roots:
Let alpha and beta be the roots of the given quadratic equation.
Quadratic Equation:
The equation whose roots are alpha^2 and beta^2 can be found using Vieta's formulas.
Vieta's formulas state that the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a and the product of the roots is c/a.
Finding New Equation:
Let the new equation be x^2 + px + q = 0 with roots alpha^2 and beta^2.
According to Vieta's formulas, we have:
alpha^2 + beta^2 = p
alpha^2 * beta^2 = q
Substitute Roots:
Substitute the values of alpha and beta into the above equations to find the new coefficients p and q.
Final Equation:
The equation with roots alpha^2 and beta^2 will be x^2 - (alpha + beta)x + alpha*beta = 0.
Therefore, the equation whose roots are alpha^2 and beta^2 is x^2 - (alpha + beta)x + alpha*beta = 0.
4x^2 + 7x + 2 = 0
Finding Roots:
Using the quadratic formula, we can find the roots of the given equation as alpha and beta.
Roots:
Let alpha and beta be the roots of the given quadratic equation.
Quadratic Equation:
The equation whose roots are alpha^2 and beta^2 can be found using Vieta's formulas.
Vieta's formulas state that the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a and the product of the roots is c/a.
Finding New Equation:
Let the new equation be x^2 + px + q = 0 with roots alpha^2 and beta^2.
According to Vieta's formulas, we have:
alpha^2 + beta^2 = p
alpha^2 * beta^2 = q
Substitute Roots:
Substitute the values of alpha and beta into the above equations to find the new coefficients p and q.
Final Equation:
The equation with roots alpha^2 and beta^2 will be x^2 - (alpha + beta)x + alpha*beta = 0.
Therefore, the equation whose roots are alpha^2 and beta^2 is x^2 - (alpha + beta)x + alpha*beta = 0.
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If alpha and beta are the roots of 4x square plus 7xplus 2=0 then the equation whose roots are alpha square and beta square is?
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If alpha and beta are the roots of 4x square plus 7xplus 2=0 then the equation whose roots are alpha square and beta square is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If alpha and beta are the roots of 4x square plus 7xplus 2=0 then the equation whose roots are alpha square and beta square is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the roots of 4x square plus 7xplus 2=0 then the equation whose roots are alpha square and beta square is?.
If alpha and beta are the roots of 4x square plus 7xplus 2=0 then the equation whose roots are alpha square and beta square is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If alpha and beta are the roots of 4x square plus 7xplus 2=0 then the equation whose roots are alpha square and beta square is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the roots of 4x square plus 7xplus 2=0 then the equation whose roots are alpha square and beta square is?.
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