Question 9
Which of the following equation has two distinct real roots?
(a) $2 x^{2} - 3 \sqrt{2} x + \frac{9}{4} = 0$
(b) $x^{2} + x - 5 = 0$
(c) $x^{2} + 3 x + 2 \sqrt{2} = 0$
(d) $5 x^{2} - 3 x + 1 = 0$

Join BYJU'S Learning Program

x3−5x2+2x−10=0For what real value of x is the equation above true?

The correct option is D 5Solve the above equation as follows:x3−5x2+2x−10=0x2(x−5)+2(x−5)=0x2+2=0 and x−5=0x2=−2 and x=5Since x2=−2 implies the imaginary value of x, therefore real value of x is 5.

$x^{3} - 5 x^{2} + 2 x - 10 = 0$
For what real value of $x$ is the equation above true?

The correct option is D $5$
Solve the above equation as follows:
$x^{3} - 5 x^{2} + 2 x - 10 = 0$
$x^{2} (x - 5) + 2 (x - 5) = 0$
$x^{2} + 2 = 0$ and $x - 5 = 0$
$x^{2} = - 2$ and $x = 5$
Since $x^{2} = - 2$ implies the imaginary value of $x$ , therefore real value of $x$ is $5$ .