The quadratic polynomial p ( x ) has the following properties: p ( x ) ≥ 0 for all real numbers, p (1)= 0 and p(2)=2. Find the value of p(0)+p(3).

Question

The quadratic polynomial p ( x ) has the following properties: p ( x ) ≥ 0 for all real numbers, p (1)= 0 and p(2)=2. Find the value of p(0)+p(3). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

as P (1)=0 text and p ( x ) ≥ 0 text hence let p ( x )= k ( x -1)2, k >0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/50f64bb5870fed4031aa3a626c29c1df-.png" /> p (2)= k =2 ⇒ k =2 ∴ p ( x )=2( x -1)2 ⇒ p (0)+ p (3)=10

Q. The quadratic polynomial $p (x)$ has the following properties: $p (x) \geq 0$ for all real numbers, $p (1) =$ 0 and $p (2) = 2$ . Find the value of $p (0) + p (3)$ .

as $P (1) = 0$
$and p (x) \geq 0 hence let p (x) = k (x - 1)^{2}, k > 0$

$p (2) = k = 2 \Rightarrow k = 2$
$∴ p (x) = 2 (x - 1)^{2} \Rightarrow p (0) + p (3) = 10$

Q. The quadratic polynomial p(x) has the following properties: p(x)≥0 for all real numbers, p(1)= 0 and p(2)=2. Find the value of p(0)+p(3).

as P(1)=0 and p(x)≥0 hence let p(x)=k(x−1)2,k>0 p(2)=k=2⇒k=2 ∴p(x)=2(x−1)2⇒p(0)+p(3)=10

Q. The quadratic polynomial $p (x)$ has the following properties: $p (x) \geq 0$ for all real numbers, $p (1) =$ 0 and $p (2) = 2$ . Find the value of $p (0) + p (3)$ .

as $P (1) = 0$
$and p (x) \geq 0 hence let p (x) = k (x - 1)^{2}, k > 0$

$p (2) = k = 2 \Rightarrow k = 2$
$∴ p (x) = 2 (x - 1)^{2} \Rightarrow p (0) + p (3) = 10$