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Relationship Between Zeroes and Coefficients of a Quadratic Polynomial

If α&β are ze...

Question

If $α & β$ are zeros of p(x) and $α + β = 24 & α - β = 8$ , then find quadratic polynomial.

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Solution

$α + β = 24$ - - - - (a)
$α - β = 8$ - - - - (b)
Add (a) and (b) we get,
$α + β + α - β = 24 + 8$
$2 α = 32$
$α = 16$ - - - - (c)
Substitute the value of $α$ (from (c)) in equation (a)
$16 + β = 24$
$\Rightarrow β = 8$
$∴ α = 16$ and $β = 8$
The required quadratic equation is $x^{2}$ - (sum of zeroes) x + Product of zeroes
$= x^{2} - (α + β) x + α \times β$
$= x^{2} - (16 + 8) x + (16 \times 8)$
$= x^{2} - 24 x + 128$

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