Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively: $4, 1$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) Let the quadratic polynomial be $p(x) = ax^2 + bx + c$,where $\alpha$ and $\beta$ are its zeroes.
The sum of the zeroes is given by $\alpha + \beta = 4 = \frac{4}{1} = \frac{-b}{a}$.
The product of the zeroes is given by $\alpha \times \beta = 1 = \frac{1}{1} = \frac{c}{a}$.
By comparing the ratios,if we assume $a = 1$,then $b = -4$ and $c = 1$.
Substituting these values into the general form $ax^2 + bx + c$,we get the quadratic polynomial $x^2 - 4x + 1$.

Explore More

Similar Questions

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

If $2x^3 - x^2 - 2x - 8$ is divided by $x - 2$,then the quotient polynomial is............

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

Verify that $\frac{-2}{3}$ is a zero of the linear polynomial $p(x)=3x+2$.

Every quadratic polynomial has at the most ......... zero/s.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo