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Discriminant

State whether...

Question

State whether $2 x^{2} - 6 x + \frac{9}{2} = 0$ has two distinct real roots. Justify your answer.

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Solution

Given,

$2 x^{2} - 6 x + \frac{9}{2} = 0$

$\Rightarrow 4 x^{2} - 12 x + 9 = 0$

$(2 x - 3)^{2} = 0$

$2 x - 3 = 0$

$∴ x = \frac{3}{2}$

The given quadratic equation has equal roots.

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Q. (1)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(i)

x^{2} - 3 x + 4 = 0

(2)
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2 x^{2} - 6 x + 3 = 0

.

Question 2 (ii)
Write whether the given statement is true or false. Justify your answer.
Every quadratic equation has at least one real roots.

Q. Question 2 (ii)
Write whether the following statements are true or false. Justify your answers.
Every quadratic equation has at least one real root.

Q. Check whether the following statement is true of false. Justify your answer.

"Every quadratic equation has at least one real root".

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