If 9 and -5 are zeroes of the polynomial $x^{2} + (a + 5) x - b$ , then find the value of a and b. [2 MARKS]

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Solution

Concept : 1 Mark
Calculation : 1 Mark

Given polynomial is,

$x^{2} + (a + 5) x - b$

$\Rightarrow α + β = \frac{- b}{a} = \frac{- (a + 5)}{1}$

$\Rightarrow \frac{- (a + 5)}{1} = 9 - 5$

$a + 5 = - 4$

$\Rightarrow a = - 9$

Also,

$α β = \frac{c}{a} = \frac{- b}{1}$

$\Rightarrow \frac{- b}{1} = 9 \times (- 5)$

$\Rightarrow - b = - 45$

$\Rightarrow b = 45$

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