Write the Quadratic polynomial whose
zeros are -3 and 2 ? *
Answers
Answer:
x² + x - 6 = 0
Explanation:
Let,
α = -3
β = 2
α + β = -3 + 2 = -1
α β = ( -3 ) x 2 = -6
x² - ( α + β )x + α β = 0
= > x² - ( -1 )x + ( -6 ) = 0
= > x² + x - 6 = 0
Therefore, the Quadratic polynomial is x² + x - 6 = 0
The required quadratic equation is x²+x-6 = 0.
Given:
The zeros of a polynomial are -3 and 2.
To Find:
The quadratic polynomial.
Solution:
To solve this problem, we need to understand the following concepts:
1) A quadratic equation refers to an equation having degree 2 and that has the general form ax²+bx+c=0.
2) Zeros of a polynomial refer to those values of 'x' for which the value of the polynomial p(x) = 0.
Now, we are given two zeros of an unknown polynomial, -3 and 2.
We need to construct the quadratic equation out of it.
Since -3 and 2 are roots of the polynomial, we can write
x = -3 and x = 2.
⇒ x-(-3) = 0 and x-2 = 0
⇒ x+3=0 and x-2=0
Now, to find a quadratic polynomial, we will multiply the above two equations involving the roots of the required quadratic polynomial.
⇒ (x+3)(x-2) = 0
Solving the above equation, we have:
x²+3x-2x-6 = 0
⇒ x²+x-6 = 0
Hence, the required quadratic equation is x²+x-6 = 0.
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