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Find the quadratic polynomial whose zero...

Find the quadratic polynomial whose zeros are 2 and -6.verify the relation between the coefficients and the zeros of the polynomial.

Text Solution

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Let `alpha and beta` are the roots such that `alpha = 2` and `beta = -6`.
Here, sum of roots, `alpha+beta = 2+(-6) = -4`
Product of roots, `alphabeta = 2**-6 = -12`
Quadratic equation can be given as,
`x^2-(alpha+beta)x+alphabeta = 0`
`=>x^2+4x-12 = 0`
so, the quadratic polynomial will be `x^2+4x-12`.
Now, we will verify the relation between zeroes and coefficients of this polynomial.
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