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Find the quadratic polynomial is 2,-6 verify the relation between cofficient and the zeroes of the following
if x +a is a factor of 2x square +,2ax+5x+10?
if x +a is a factor of 2x square +,2ax+5x+10?
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Find the quadratic polynomial is 2,-6 verify the relation between coff...
Quadratic Polynomial with given zeroes
To find the quadratic polynomial with zeroes 2 and -6, we can use the factored form of a quadratic equation. The factored form is given by:
(x - r1)(x - r2) = 0
Where r1 and r2 are the zeroes of the quadratic polynomial. Substituting the given zeroes, we get:
(x - 2)(x + 6) = 0
Expanding this equation gives us:
x^2 + 6x - 2x - 12 = 0
x^2 + 4x - 12 = 0
Therefore, the quadratic polynomial with zeroes 2 and -6 is x^2 + 4x - 12.
Relation between coefficient and zeroes
Given the quadratic polynomial 2x^2 + 2ax + 5x + 10, we are told that x + a is a factor. This means that if x + a is a factor, then a is a root of the polynomial.
To verify this, we substitute x = -a into the polynomial and see if it equals zero:
2(-a)^2 + 2a(-a) + 5(-a) + 10 = 0
2a^2 - 2a^2 - 5a + 10 = 0
-5a + 10 = 0
-5a = -10
a = 2
Therefore, the coefficient 'a' is 2, which is one of the zeroes of the polynomial. This verifies the relation between the coefficient and zeroes of the given polynomial.
To find the quadratic polynomial with zeroes 2 and -6, we can use the factored form of a quadratic equation. The factored form is given by:
(x - r1)(x - r2) = 0
Where r1 and r2 are the zeroes of the quadratic polynomial. Substituting the given zeroes, we get:
(x - 2)(x + 6) = 0
Expanding this equation gives us:
x^2 + 6x - 2x - 12 = 0
x^2 + 4x - 12 = 0
Therefore, the quadratic polynomial with zeroes 2 and -6 is x^2 + 4x - 12.
Relation between coefficient and zeroes
Given the quadratic polynomial 2x^2 + 2ax + 5x + 10, we are told that x + a is a factor. This means that if x + a is a factor, then a is a root of the polynomial.
To verify this, we substitute x = -a into the polynomial and see if it equals zero:
2(-a)^2 + 2a(-a) + 5(-a) + 10 = 0
2a^2 - 2a^2 - 5a + 10 = 0
-5a + 10 = 0
-5a = -10
a = 2
Therefore, the coefficient 'a' is 2, which is one of the zeroes of the polynomial. This verifies the relation between the coefficient and zeroes of the given polynomial.
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Find the quadratic polynomial is 2,-6 verify the relation between cofficient and the zeroes of the following if x +a is a factor of 2x square +,2ax+5x+10?
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Find the quadratic polynomial is 2,-6 verify the relation between cofficient and the zeroes of the following if x +a is a factor of 2x square +,2ax+5x+10? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the quadratic polynomial is 2,-6 verify the relation between cofficient and the zeroes of the following if x +a is a factor of 2x square +,2ax+5x+10? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the quadratic polynomial is 2,-6 verify the relation between cofficient and the zeroes of the following if x +a is a factor of 2x square +,2ax+5x+10?.
Find the quadratic polynomial is 2,-6 verify the relation between cofficient and the zeroes of the following if x +a is a factor of 2x square +,2ax+5x+10? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the quadratic polynomial is 2,-6 verify the relation between cofficient and the zeroes of the following if x +a is a factor of 2x square +,2ax+5x+10? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the quadratic polynomial is 2,-6 verify the relation between cofficient and the zeroes of the following if x +a is a factor of 2x square +,2ax+5x+10?.
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