Obtain a quadratic polynomial with the follow | vedclass

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

Question

(D) quadratic polynomial is given by the formula $p(x) = k[x^{2} - (	ext{sum of zeros})x + (	ext{product of zeros})]$,where $k$ is a non-zero real c

Vedclass · Accepted Answer

$k(4x^{2} + x + 1)$

Vedclass · Answer

(D) quadratic polynomial is given by the formula $p(x) = k[x^{2} - (	ext{sum of zeros})x + (	ext{product of zeros})]$,where $k$ is a non-zero real constant.Given that the sum of the zeros $= -\frac{1}{4}$ and the product of the zeros $= \frac{1}{4}$.Substituting these values into the formula:$p(x) = k[x^{2} - (-\frac{1}{4})x + \frac{1}{4}]$$p(x) = k[x^{2} + \frac{1}{4}x + \frac{1}{4}]$To simplify,we can take $k = 4$ (or any multiple of $4$):$p(x) = 4[x^{2} + \frac{1}{4}x + \frac{1}{4}]$$p(x) = 4x^{2} + x + 1$Thus,the general form is $k(4x^{2} + x + 1)$.

Obtain a quadratic polynomial with the following conditions:
The sum of the zeros $= -\frac{1}{4}$;
The product of the zeros $= \frac{1}{4}$.

Similar Questions

Draw the graph of $p(x) = 2x - 5$ and find the zeros of this polynomial.

The total cost of $(x+1)$ cameras is ₹ $(x^{3}+3x^{2}+5x+3)$. Find the cost of one camera.

Divide $x^{4}+2x^{3}+3x^{2}+2x+20$ by $x^{2}+2x+2$.

If the remainder on division of $x^{3}+2 x^{2}+k x+3$ by $x-3$ is $21$,find the quotient and the value of $k$. Hence,find the zeroes of the cubic polynomial $x^{3}+2 x^{2}+k x-18$.

State the degree of the given polynomial: $p(x) = \frac{7}{2} x - 9$

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Obtain a quadratic polynomial with the following conditions:The sum of the zeros $= -\frac{1}{4}$;The product of the zeros $= \frac{1}{4}$.