Find the zeros of the quadratic polynomial $p(x) = 10x^2 - 14x - 12$ and also find the sum and the product of the zeros of the polynomial.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Given polynomial is $p(x) = 10x^2 - 14x - 12$.
To find the zeros,we factorize the polynomial:
$10x^2 - 14x - 12 = 10x^2 - 20x + 6x - 12$
$= 10x(x - 2) + 6(x - 2)$
$= (10x + 6)(x - 2)$
Setting $p(x) = 0$,we get $(10x + 6)(x - 2) = 0$.
This gives $x = -6/10 = -3/5$ or $x = 2$.
Thus,the zeros are $-3/5$ and $2$.
Using the relationship between zeros and coefficients for $ax^2 + bx + c$:
Sum of zeros $= -b/a = -(-14)/10 = 14/10 = 7/5$.
Product of zeros $= c/a = -12/10 = -6/5$.

Explore More

Similar Questions

Factorize the following polynomial: $p(x) = 25x^2 - 40x + 16$.

If the product of the zeros of $p(x) = ax^{2} - 6x - 6$ is $4$,then $a = $ ............

Obtain the quadratic or the cubic polynomial as the case may be in the standard form with the following coefficients: $a=6, b=-7, c=-3$.

Find the zeros of the following quadratic polynomial: $5x^2 + 8x + 3$.

Identify the type of the given polynomial based on its degree: $p(x) = 2012x + 2011$.

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