If roots of $p x^{2} + q x + 1 = 0$ are equal, then

p^{2} - 4 p = 0

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

q^{2} - 4 p = 0

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

p^{2} - 4 q = 0

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

None of these

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

Open in App

Solution

The correct option is B $q^{2} - 4 p = 0$
Nature of roots
When the co-efficients of a quadratic equation are real, then the nature of the roots is as follows
Complex roots: If $D < 0$ , then the roots are complex of the form $A \pm i B .$
Real Roots: If $D > 0$ , then the roots are real and distinct.
For the particular case, when $D = 0$ the roots are real and equal

As mentioned above, when roots are real and equal
Then, $D = 0$ $\Rightarrow q^{2} - 4 p = 0$

Suggest Corrections

Similar questions

Q. Let

p, q \in R

. If

2 - \sqrt{3}

is a root of the quadratic equation

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

, then

If the roots of the quadratic equation $x^{2} + (p + 2) x + (2 p + 5) = 0$ is real. Which of the following is true?

If $α$ be a real root of the equation $x^{3} + p x^{2} + q x + r = 0$ where p, q and r are real. If $p^{2} - 4 q - 2 p α - 3 α^{2} \geq 0$ then other roots are ________.

Q. If

cos α

and

sin α

are the roots of the quadratic equation

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

, then the value of

p^{2} - q^{2} + 2 p r

is equal to

Q. If α, β are the roots of the equation

x^{2} + p x + 1 = 0; γ, δ

the roots of the equation

x^{2} + q x + 1 = 0, t h e n (α - γ) (α + δ) (β - γ) (β + δ) =

(a)

q^{2} - p^{2}

(b)

p^{2} - q^{2}

(c)

p^{2} + q^{2}

(d) none of these.

Join BYJU'S Learning Program

If roots of px2+qx+1=0 are equal, then

If roots of $p x^{2} + q x + 1 = 0$ are equal, then