Question

If zero of the polynomial x2+px+q are 3 and 2 find the value of p and q​

Answer 1

Step-by-step explanation:

P ( 2 )

= (2)^2 - 2p = q

= 4 - 2p = q ... ( 1)

P(3)

= (3)^2 - 3p = q

= 9 - 3p = q. ...... (2)

From 1 and 2 ..

4 - 2p = 9 - 3p

4 - 9 = -3p + 2p

-5 = -p

p = 5 Ans.

Q = 4 - 2p = 4 - 2*5 = -6

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Answer 2

Answer:

The value of 'p' = -5 and the value of 'q' = 6

Step-by-step explanation:

Given,

2 and 3 are the zeros of the polynomial  x²+px+q

To find,

The value of 'p' and 'q'

Recall the concept

If x = a is a zero of the polynomial p(x), then p(a) = 0

Solution:

Let p(x) = x²+px+q

Since 2 is a zero of the polynomial, we have p(2) = 0

p(2) = 0 ⇒ 2²+2p+q = 0

⇒ 4 + 2p + q = 0

2p + q = -4 ---------------(1)

Also, since 3 is a zero of the polynomial, we have p(3) = 0

p(3) = 0 ⇒ 3²+3p+q = 0

⇒ 9+3p+q = 0

⇒ 3p+q = -9 --------------(2)

Subtracting (1) from (2) we get

(2) - (1) → (3p - 2p) = (-9-(-4)

p = -5

substituting the value of p = -5 in equation (1) we get

2(-5) + q = -4

-10 + q = -4

q = -4+ 10

q = 6

∴The value of 'p' = -5 and the value of 'q' = 6

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