10 X − 1 X = 3

`10x -(1)/x` = 3

Sum

`10x -(1)/x` = 3

⇒ `(10x^2 - 1)/x` = 3

⇒ 10x² - 3x -1 = 0
⇒ 10x² - 5x + 2x - 1 = 0
⇒ 5x(2x - 1) + 1(2x - 1) = 0
⇒ (2x - 1)(5x + 1) = 0
⇒ 2x - 1 = 0 or 5x + 1 = 0

x = `(1)/(2)` or x = `- (1)/(5)` are two roots of the equation.

shaalaa.com

Is there an error in this question or solution?

Find the values of k for which the roots are real and equal in each of the following equation:

x² - 2kx + 7k - 12 = 0

Solve for x :

x² + 5x − (a² + a − 6) = 0

Find the value of the discriminant in the following quadratic equation :

`4 sqrt 3 "x"^2 + 5"x" - 2 sqrt 3 = 0`

Determine the nature of the roots of the following quadratic equation :

x² +3x+1=0

Find the value of k for which the following equation has equal roots:
(k − 12)x²+ 2(k − 12)x + 2 = 0.

Form the quadratic equation whose roots are:
`sqrt(3) and 3sqrt(3)`

Given that one root of the quadratic equation ax² + bx + c = 0 is three times the other, show that 3b² – 16ac.

Choose the correct answer from the given four options :

The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)

If –5 is a root of the quadratic equation 2x² + px – 15 = 0, then:

State whether the following quadratic equation have two distinct real roots. Justify your answer.

2x² + x – 1 = 0