MyQuestionIcon

3

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Harmonic Mean

Find the coef...

Question

Find the coefficients of the equation $x^{2} + p x + q = 0$ such that its roots are equal to $p$ and $q$ .

Open in App

Solution

Suppose the root of the equation is alpha and beta.
We know that sum of the root is = $α + β .$ (roots are equal p and q)
But $p = p + q$
Therefor $q = 0$ .
The product of the root = $α \times β$
$q = p . q$
Hence $p = 1$
Hence the cofficient of the equation is $1, 1, 0$

Suggest Corrections

thumbs-up

0

Similar questions

α

β

of the equation

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

3 α + 4 β = 7

5 α - β = 4

(p, q)

p, q

are the roots of equation

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

, then the value of

p

must be equal to

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

x^{2} + q x + p = 0, (p \neq q)

have a common root, show that

1 + p + q = 0

; show that their other roots are the roots of the equation

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

p

q

are roots of the equation

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

Q. If p and q are the roots of the equation

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

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Harmonic Progression

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon