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.

(v)

The condition (x + 4)2 – 8x = 0 has no genuine roots.

Working on the above condition,

$x2\text{ }+\text{ }8x\text{ }+\text{ }16\text{ }\text{ }8x\text{ }=\text{ }0$

$x2\text{ }+\text{ }16\text{ }=\text{ }0$

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

= (0) – 4(1) (16) < 0

Subsequently, the roots are nonexistent.

(vi)

The condition (x – √2)2 – √2(x+1)=0 has two unmistakable and genuine roots.

Improving on the above condition,

$x2\text{ }\text{ }2\surd 2x\text{ }+\text{ }2\text{ }\text{ }\surd 2x\text{ }\text{ }\surd 2\text{ }=\text{ }0$

$x2\text{ }\text{ }\surd 2\left( 2+1 \right)x\text{ }+\text{ }\left( 2\text{ }\text{ }\surd 2 \right)\text{ }=\text{ }0$

$x2\text{ }\text{ }3\surd 2x\text{ }+\text{ }\left( 2\text{ }\text{ }\surd 2 \right)\text{ }=\text{ }0$

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

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

$=\text{ }18\text{ }\text{ }8\text{ }+\text{ }4\surd 2\text{ }>\text{ }0$

Subsequently, the roots are genuine and unmistakable.

i

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