Question

Which of the following statement is not true?
A quadratic equation always has two roots.
Roots of a quadratic equation can never be zero.
If the discriminant of a quadratic equation is less than zero it has no real roots.
If the discriminant of a quadratic equation is zero it has two real and equal roots.

Answer 1

Answer:

hey mate here is your answer

Step-by-step explanation:

c is the answer

Answer 2

The statement which is not true about quadratic equations is:

(b) Roots of a quadratic equation can never be zero.

Given:

• a) A quadratic equation always has two roots.
• b) Roots of a quadratic equation can never be zero.
• c) If the discriminant of a quadratic equation is less than zero it has no real roots.
• d) If the discriminant of a quadratic equation is zero it has two real and equal roots.

To find:

• Which of the statements is not true about quadratic equations?

Solution:

The statement which is not true about quadratic equations is: :Roots of a quadratic equation can never be zero.

Because roots of quadratic equations can be zero.

Thus,

Option (b) is not true about quadratic equations.

Let us check,why the other options are correct in regards of quadratic equations.

Option (a): A quadratic equation always has two roots.

Yes, it is correct.

As the degree of quadratic equation is 2, it can always have two roots, equal or distinct.

Option (c):If the discriminant of a quadratic equation is less than zero it has no real roots.

Yes, it is correct.

As, we know that,

If D<0, then the quadratic equation has imaginary or complex roots.

For example

${x}^{2} - 4x + 9 = 0$

here

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

$\implies\: D =( - {4)}^{2} - 4(1)(9)$

$\implies\: D = 16 - 36$

$\implies\: D = - 20$

here,

$D< 0$

In this case the quadratic equation has no real roots exist.

Option (d) :If the discriminant of a quadratic equation is zero it has two real and equal roots.

Yes, it is correct.

As, we know,

If D=0, then the quadratic equation has two equal roots

For Example

${x}^{2} - 2x + 1 = 0$

$D = ( { - 2)}^{2} - 4(1)(1)$

$\implies\: D = 4 - 4$

$\implies\: D = 0$

Thus,

In this case quadratic equation has two real and equal roots.

Thus,

The statement which is not true about quadratic equations is:

(b) Roots of a quadratic equation can never be zero.

Learn more:

1) Find the nature of roots of quadratic equation 2x sq. + 3x - 7=0

https://brainly.in/question/6314574

2) Nature of the roots of an equation 3x^2+7x+8

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