Question

Is the following statement true or false, justify the answer. If in a quadratic equation, the coefficient of x is zero, then the quadratic equation has no real roots.

Answer 1

Answer:

Step by step explantation

true ,beacuse if x is not there then degree become

0 then equation will not be left there. so that's why it is true. so equation have not real roots.

hope it helps you

Answer 2

Answer:

False

Let us consider an example,

$ax^{2} +0x+c=0$ (b=0)

Since, Discriminant = $b^{2}-4ac$

Case 1 : If a is positive and c is negative.

= 0 - 4(a)(-c)

= 4ac

Hence, 4ac>0 the equation has real and distinct roots.

Case 2 : If a is negative and c is positive.

= 0 - 4(-a)(c)

= 4ac

Hence, 4ac>0 the equation has real and distinct roots.

Case 3 : If a and b both are positive or both are negative then the discriminant would be negative and in those case roots will be imaginary(no real roots).

Therefore, in two conditions real and distinct roots can be obtained even after the coefficient of x being 0.