If the zeroes of the quadratic polynomial x^{ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $p(x) = x^{2} + (a+1)x + b$.Given that $2$ and $-3$ are the zeroes of the quadratic polynomial $p(x)$.Therefore,$p(2) = 0$ and $p(-3) = 0$.For

Vedclass · Accepted Answer

$a=0, b=-6$

Vedclass · Answer

(A) Let $p(x) = x^{2} + (a+1)x + b$.Given that $2$ and $-3$ are the zeroes of the quadratic polynomial $p(x)$.Therefore,$p(2) = 0$ and $p(-3) = 0$.For $x = 2$:$2^{2} + (a+1)(2) + b = 0$$4 + 2a + 2 + b = 0$$2a + b = -6$ ..... $(i)$For $x = -3$:$(-3)^{2} + (a+1)(-3) + b = 0$$9 - 3a - 3 + b = 0$$-3a + b = -6$ ..... $(ii)$Subtracting equation $(ii)$ from equation $(i)$:$(2a + b) - (-3a + b) = -6 - (-6)$$2a + b + 3a - b = 0$$5a = 0 \Rightarrow a = 0$.Substituting $a = 0$ in equation $(i)$:$2(0) + b = -6 \Rightarrow b = -6$.Thus,the required values are $a = 0$ and $b = -6$.

If the zeroes of the quadratic polynomial $x^{2}+(a+1)x+b$ are $2$ and $-3$,then

Similar Questions

The value of $p(x) = 3x^2 + 7x + 4$ at $x = 1$ is:

If one of the zeroes of the quadratic polynomial $(k-1) x^{2}+k x+1$ is $-3,$ then the value of $k$ is

The value of $p(x) = 4x^3 + 3x^2 + 2x + 1$ at $x = 1$ is $\ldots \ldots \ldots$

If the zero of the polynomial $p(x) = ax^2 - 11x + 3$ is $1$,then $a = \ldots$

The sum of the zeros of a quadratic polynomial $p(x) = 3x^2 + 7x + 4$ is...........

Vedclass Test Series

Exam Paper Generator

Online Exam Module