Determine nature of roots of the quadratic equation √3 $x^{2}$ +2√3x+√3=0 ( 1 mark)

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Solution

Comparing √3 $x^{2}$ +2√3x+√3=0 with a $x^{2}$ +bx+c=0

We get a=√3, b=2√3, c=√3

Now, $b^{2}$ -4ac= ${(2 \sqrt{3})}^{2}$ -4×√3×√3

=4×3 -4×3

=12-12

=0

Roots of the equation are real and equal.

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Determine nature of roots of the quadratic equation √3 x2+2√3x+√3=0 ( 1 mark)

Comparing √3x2 +2√3x+√3=0 with ax2+bx+c=0 We get a=√3, b=2√3, c=√3 Now, b2-4ac=(2√3)2-4×√3×√3 =4×3 -4×3 =12-12 =0 Roots of the equation are real and equal.

Determine nature of roots of the quadratic equation √3 $x^{2}$ +2√3x+√3=0 ( 1 mark)

Comparing √3 $x^{2}$ +2√3x+√3=0 with a $x^{2}$ +bx+c=0

We get a=√3, b=2√3, c=√3

Now, $b^{2}$ -4ac= ${(2 \sqrt{3})}^{2}$ -4×√3×√3

=4×3 -4×3

=12-12

=0

Roots of the equation are real and equal.