Book Online Demo

Check Your IQ

Try Test

Courses

If -5 is a root of the quadratic equation $2 x^{2} + px - 15 = 0$ and the quadratic equation $p (x^{2} + x) + k = 0$ has equal roots, then the value of $k$ is:

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

\frac{4}{7}

\frac{2}{7}

\frac{1}{5}

\frac{7}{4}

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

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

Take Free Test

Detailed Solution

Given quadratic equations are,

2 x^{2} + px - 15 = 0

and

p (x^{2} + x) + k = 0

.
-5 is the root of the equation

2 x^{2} + px - 15 = 0

then,

2 {(- 5)}^{2} + p (- 5) - 15 = 0

⟹ 50 - 5 p - 15 = 0

⟹ 35 - 5 p = 0

⟹ 35 = 5 p

⟹ p = 7

….(1)
And quadratic equation

p (x^{2} + x) + k = 0

has equal roots.
We know that, when roots of the equation are equal then,
Discriminant

(D) = b^{2} - 4 ac = 0

.
Here,

a = p, b = p, c = k

.
Then,

b^{2} - 4 ac = 0

⟹ p^{2} - 4 \times p \times k = 0

⟹ {(7)}^{2} - 4 \times 7 \times k = 0

{Using (1)}

⟹ 49 - 28 k = 0

⟹ 49 = 28 k

⟹ k = \frac{49}{28}

∴ k = \frac{7}{4}

∴ The value of k is

\frac{7}{4}

.
Hence, the correct option is 1.

Watch 3-min video & get full concept clarity