Question

Find the zeroes of the Polynomial P(x) = x2 + 2x - 15 and verify the relationship between the

zeroes andcoefficients.​

Answer 1

Answer:

Given Polynomial : x² + 2x -15

Finding Zeroes:

$: { \implies{ \sf{ {x}^{2} + 2x - 15 }}} \\ \\ : { \implies{ \sf{ {x}^{2} - 3x + 5x - 15 }}} \\ \\ : { \implies{ \sf{x(x - 3) + 5(x - 3)}}} \\ \\ : { \implies{ \sf{(x + 5)(x - 3) = 0}}} \\ \\ : { \implies{ \sf{x = - 5 \: or \: 3}}}$

Relationship between zeroes and coefficients:-

Let us take, Alpha = -5 and beta = 3

From the polynomial, x² + 2x - 15

• a = 1, b = 2 , c = -15

$\sf \: sum \: of \: zeroes = \alpha + \beta = \frac{ - b}{a} \\ \\ - 5 + 3 = \frac{ - 2}{1} \\ \\ - 2 = - 2$

$\sf product \: of \: zeroes = \alpha \beta = \frac{c}{a} \\ \\ - 5(3) = \frac{ - 15}{1} \\ \\ - 15 = - 15$

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