CameraIcon

SearchIcon

MyQuestionIcon

2

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Nature of Roots

If the roots ...

Question

If the roots of the equation $x^{2} - (p + 4) x + 2 p + 5 = 0$ are equal, then the value(s) of $p$ is/are

A

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

- 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

- 2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct options are
A $2$
C $- 2$
$x^{2} - (p + 4) x + 2 p + 5 = 0$
As roots are equal, so
$D = 0 \Rightarrow (p + 4)^{2} - 4 (2 p + 5) = 0 \Rightarrow p^{2} + 8 p + 16 - 8 p - 20 = 0 \Rightarrow p^{2} - 4 = 0 \Rightarrow p = \pm 2$

Suggest Corrections

thumbs-up

14

Similar questions

Q. The value of p and q (p ≠ 0, q ≠ 0) for which p, q are the roots of the equation

x^{2} + p x + q = 0

are
(a) p = 1, q = −2
(b) p = −1, q = −2
(c) p = −1, q = 2
(d) p = 1, q = 2

p, q

are the roots of the equation

x^{2} + p x + q = 0

Q. If the roots of the equation

x^{2} - (p + 4) x + 2 p + 5 = 0

are equal, then the value(s) of

p

Q. If roots of equation of

x^{2} + x + 1 = 0

a, b

x^{2} + p x + q = 0

\frac{a}{b}, \frac{b}{a}

p + q

tan 25^{\circ}

tan 20^{\circ}

are the roots of

x^{2} + 2 p x + q = 0

, then the value of

2 p - q

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Nature of Roots

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon