If (x +5) and (x -3) are the factors of $a x^{2} + b x + c,$ , then values of a, b and c are

1,-2,15

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1,2,-15

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1,2,15

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1,2,3

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Solution

The correct option is B 1,2,-15
Given that,
x+5 is a factor,
Let's take $p (x) = a x^{2} + b x + c S u b s t i t u t e x = - 5 p (- 5) = a {(- 5)}^{2} + b (- 5) + c = 25 a - 5 b + c = 0 . . . . . . . . . . . (1)$
Also x - 3 is a factor.
$p (3) = a {(3)}^{2} + 3 b + c = 0 c = - 9 a - 3 b S u b s t i t u t e t h i s i n (1) 25 a - 5 b = 9 a + 3 b 25 a - 9 a = 3 b + 5 b 16 a = 8 b \frac{a}{b} = \frac{8}{16} = \frac{1}{2} S u b s t i t u t e a = 1 a n d b = 2 i n (1) 25 (1) - 5 (2) = - c c = - 15 a = 1, b = 2 a n d c = - 15 H e n c e o p t i o n C i s t h e c o r r e c t a n s w e r .$

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Similar questions

a x^{2} + b x + c

If both $(3 x + 2)$ and $(x + 3)$ are factors of $a x^{2} + b x + c$ then find the value of $a + b + c$ .

(x + 3)

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a x^{2} + b x + 5

10 a - 3 b + 1

(x - 1)

(x - 2)

p (x) = x^{3} + a x^{2} + b x + c

a + b = 1

b

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