The number of polynomials having zeroes as -2 | vedclass

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

Question

(B) Let $p(x) = a(x^2 - (	ext{sum of zeroes})x + (	ext{product of zeroes}))$ be the general form of the polynomial.Given zeroes are $\alpha = -2$ an

Vedclass · Accepted Answer

more than $3$

Vedclass · Answer

(B) Let $p(x) = a(x^2 - (	ext{sum of zeroes})x + (	ext{product of zeroes}))$ be the general form of the polynomial.Given zeroes are $\alpha = -2$ and $\beta = 5$.Sum of zeroes $= \alpha + \beta = -2 + 5 = 3$.Product of zeroes $= \alpha \cdot \beta = -2 	imes 5 = -10$.Thus, the polynomial is of the form $p(x) = a(x^2 - 3x - 10)$, where $a$ is any non-zero real constant.Since $a$ can take any non-zero real value (e.g., $1, 2, 3, \dots, 0.5, \dots$), there are infinitely many such polynomials.Therefore, the number of such polynomials is more than $3$.

The number of polynomials having zeroes as $-2$ and $5$ is

Similar Questions

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

Draw the graph of $p(x) = 3 - 2x - x^2$ and find the zeros of this polynomial.

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

From the given figure,find the number of real zeros of the polynomial $y = p(x)$:

One of the factors of $\ldots \ldots \ldots \ldots$ is $(x-1).$

Vedclass Test Series

Exam Paper Generator

Online Exam Module