AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

The roots of the equation $15 x^{2} - 28 = x$ are [[1]] and [[2]].

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

answer is 7 5, - 4 3.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

The roots of the equation

15 x^{2} - 28 = x

are

\frac{7}{5}

and

- \frac{4}{3}

.
Given quadratic equation is,

15 x^{2} - 28 = x

\Rightarrow 15 x^{2} - x - 28 = 0

We know that,
Discriminant for the quadratic equation

a x^{2} + bx + c = 0, a \neq 0

where a, b and c are real numbers is given by,

D = b^{2} - 4 ac

.
On comparing the given equation

15 x^{2} - x - 28 = 0

with standard form we get,

a = 15, b = - 1, c = 28

Then,

D = b^{2} - 4 ac

⟹ D = {(- 1)}^{2} - 4 \times (- 15) \times 28

⟹ D = 1 + 1680

⟹ D = 1681 > 0

Discriminant is greater than zero which means the roots of the equation exist.
Since, quadratic formula for the quadratic equation

a x^{2} + bx + c = 0, a \neq 0

where a, b and c are real numbers is given by,

x = \frac{- b \pm \sqrt{D}}{2 a}

Then,

x = \frac{- (- 1) \pm \sqrt{1681}}{2 \times 15}

⟹ x = \frac{1 \pm 41}{30}

On taking positive sign,

⟹ x = \frac{1 + 41}{30}

⟹ x = \frac{42}{30}

⟹ x = \frac{7}{5}

On taking negative sign,

⟹ x = \frac{1 - 41}{30}

⟹ x = \frac{- 40}{30}

⟹ x = \frac{- 4}{3}

Therefore, the roots of the equation

15 x^{2} - 28 = x

\frac{7}{5}

and

\frac{- 4}{3}

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!