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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.
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(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)
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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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