MyQuestionIcon

2

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

Relationship between Zeroes and Coefficients of a Polynomial

The roots x...

Question

The roots $x_{1}$ and $x_{2}$ of the equation $x^{2} + p x + 12 = 0.$ are such that $x_{2} - x_{1} = 1$ Find p.

Open in App

Solution

$x^{2} + p x + 12 = 0 s u m o f r o o t s = x_{1} + x_{2} = 12 x_{2} - x_{1} = 1 {(x_{1} + x_{2})}^{2} = {(x_{2} - x_{1})}^{2} + 4 x_{1} x_{2} p^{2} = 1 + 48 p^{2} = 49 p = \pm 7$

Suggest Corrections

thumbs-up

0

Similar questions

Q. If the roots

x_{1}

x_{2}

of the equation

x^{2} + p x + 12 = 0

possess the property

x_{1} - x_{2} = 1

, then the value of

p

x_{1}

x_{2}

are the roots of the equation

e^{2} x^{ln x} = x^{3}

x_{1} > x_{2}

x_{1}

x_{2}

be the roots of the quadratic equation

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

x_{1} = \frac{x_{2} + 4}{2 x_{2} - 1}

, then the value of

(2 q + p)

x^{3} + 5 x^{2} + p x + q = 0

x^{3} + 7 x^{2} + p x + r = 0

have two roots in common. If the third root of each equation is

x_{1}

x_{2}

, respectively, then find

- (x_{1} + x_{2})

?

Q. For the equation

{({log}_{2} x)}_{2}^{2} - 4 {log}_{2} x - m^{2} - 2 m - 13 = 0, m \in R

.
If the real roots are

x_{1}, x_{2}

x_{1} < x_{2}

, then the sum of maximum value of

x_{1}

and minimum value of

x_{2}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Relationship between Zeroes and Coefficients of a Polynomial

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Relationship between Zeroes and Coefficients of a Polynomial

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon