Question

For ax2 + bx + c = 0, which of the following statement is wrong? (a) If b2 – 4ac is a perfect square, the roots are rational. (b) If b2 = 4ac , the roots are real and equal. (c) If b2 – 4ac is negative, no real roots exist. (d) If b2 = 4ac , the roots are real and unequal.

Answer 1

Step-by-step explanation:

option D is wrong when b^2=4ac roots will be equal and real

Answer 2

For ax² + bx + c = 0,

The roots are given by

$x = \frac{ - b \: \pm \: \sqrt{ { b}^{2} - 4ac } }{2a}$

• If b² - 4ac is perfect square, then

$\sqrt{b ^{2} - 4ac}$

is rational.

Therefore, We will have rational roots.

• If b² = 4ac then,
• b² - 4ac = 0

$x = \frac{ - b \: \pm \: \sqrt{ { b}^{2} - 4ac } }{2a} \\ \\ x = \frac{ - b \pm \: 0}{2a} \\ \\ x = \frac{ - b}{2a}$

Therefore, The roots are real and equal.

• If b² - 4ac < 0, then

$\sqrt{ {b}^{2} - 4ac }$

is irrational.

So no real roots exist in this case.

Therefore, A, B, C Options are correct. Wrong statement is Option D, If b² = 4ac , the roots are real and unequal.