Let P ( x ) be a quadratic polynomial on R such that p ( x ) is negative or zero for all real number. If p(2)=0 and p(3)=-2, then p(4) is equal to

Question

Let P ( x ) be a quadratic polynomial on R such that p ( x ) is negative or zero for all real number. If p(2)=0 and p(3)=-2, then p(4) is equal to (A) -3 (B) -4 (C) -8 (D) -16

Tardigrade Admin · Accepted Answer

∵ p ( x ) is negative or zero for all real numbers and p (2)=0 ∴ p ( x )= k ( x -2)2, k <0 ∵ p (3)=-2= k (3-2)2 ⇒ k =-2 ∴ p ( x )=-2( x -2)2 ⇒ p (4)=-2 × 4=-8 .

Q. Let $P (x)$ be a quadratic polynomial on $R$ such that $p (x)$ is negative or zero for all real number. If $p (2) = 0$ and $p (3) = - 2$ , then $p (4)$ is equal to

-3

-4

-8

-16

$∵ p (x)$ is negative or zero for all real numbers and $p (2) = 0$
$∴ p (x) = k (x - 2)^{2}, k < 0$
$∵ p (3) = - 2 = k (3 - 2)^{2} \Rightarrow k = - 2$
$∴ p (x) = - 2 (x - 2)^{2} \Rightarrow p (4) = - 2 \times 4 = - 8.$

Q. Let P(x) be a quadratic polynomial on R such that p(x) is negative or zero for all real number. If p(2)=0 and p(3)=−2, then p(4) is equal to

-3

-4

-8

-16

∵p(x) is negative or zero for all real numbers and p(2)=0 ∴p(x)=k(x−2)2,k<0 ∵p(3)=−2=k(3−2)2⇒k=−2 ∴p(x)=−2(x−2)2⇒p(4)=−2×4=−8.

Q. Let $P (x)$ be a quadratic polynomial on $R$ such that $p (x)$ is negative or zero for all real number. If $p (2) = 0$ and $p (3) = - 2$ , then $p (4)$ is equal to

$∵ p (x)$ is negative or zero for all real numbers and $p (2) = 0$
$∴ p (x) = k (x - 2)^{2}, k < 0$
$∵ p (3) = - 2 = k (3 - 2)^{2} \Rightarrow k = - 2$
$∴ p (x) = - 2 (x - 2)^{2} \Rightarrow p (4) = - 2 \times 4 = - 8.$