State whether the following quadratic equations have two distinct real roots. Justify your answer.

Home » State whether the following quadratic equations have two distinct real roots. Justify your answer.

State whether the following quadratic equations have two distinct real roots. Justify your answer.

State whether the following quadratic equations have two distinct real roots. Justify your answer.

(iii)

The condition 2×2 – 6x + (9/2) = 0 has genuine and equivalent roots.

$D\text{ }=\text{ }b2\text{ }\text{ }4ac$

$=\text{ }\left( -\text{ }6 \right)2\text{ }\text{ }4\left( 2 \right)\text{ }\left( 9/2 \right)$

$=\text{ }36\text{ }\text{ }36\text{ }=\text{ }0$

Thus, the roots are genuine and equivalent.

(iv)

The condition 3×2 – 4x + 1 = 0 has two genuine and unmistakable roots.

$D\text{ }=\text{ }b2\text{ }\text{ }4ac$

$=\text{ }\left( -\text{ }4 \right)2\text{ }\text{ }4\left( 3 \right)\left( 1 \right)$

= 16 – 12 > 0

Consequently, the roots are genuine and particular.

i

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