Question

If the roots of ax2 +bx+c= 0 are real and unequal, then b2-4ac <0. Is it true?​

Answer 1

QUESTION:

If the roots of ax2 +bx+c= 0 are real and unequal, then b2-4ac <0. Is it true?

ANSWER:

If the roots of quadratic equation are real and equal then discriminant is greater than 0 so the given statement is false.

Additional information:

When;

${b}^{2} - 4ac < 0$

then it has unequal roots.

and

${b}^{2} - 4ac = 0$

then it has real and equal roots.

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Answer 2

Concept Introduction:

A mathematical statement which are made of two expression connected with a equal to sign is known as equation. The standard form of quadratic equation is ax²+bx+c = 0, where a and b are coefficients, x is variable and c is constant.

Given:

We have been given a equation,

ax²+bx+c = 0

To Find:

We have to find, whether this b²- 4ac < 0 equation is true or not.

Solution:

The roots of the equation ax²+bx+c=0 are $\frac{-b=\sqrt{b-4 a c}}{2 a}$

For, the equation to have real roots,

b²−4ac≥0

For, the equation to have unequal roots,

b²−4ac>0

So, the statement is not true.

Final Answer:

The statement is not true.

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