Question

Find the nature of the roots for the equation
$2x {}^{2} - 3x + 5 = 0$
​

Answer 1

Answer:

Analysis→

Here we're a quadratic equation 2x²-3x+5=0 and we've to find the nature of the roots of the equation. And we know that the nature of roots is depend on the Discriminant(D). And D=b²-4ac

$\:\:\:\mapsto\rm If\:D>0,\:then\:unique\:roots. \\ \mapsto\rm If\:D=0,\:then\:equal\:roots. \\ \:\:\:\:\:\:\:\:\:\:\:\mapsto\rm If\:D<0,\:then\:imaginary\:roots.$

Given→

• Equation= 2x²-3x+5
• a= 2
• b= -3
• c=5

To Find→

Nature of the roots of the equation.

Answer→

$\large{\underline{\boxed{\leadsto{\rm{Discriminant(D)=b^2-4ac}}}}}$

$\implies\rm{D=b^2-4ac}$

$\implies\rm{D=(-3)^2-4(2)(5)}$

$\implies\rm{D=9-4(10)}$

$\implies\rm{D=9-40}$

$\implies\rm{D=-31}$

${\boxed{\boxed{\implies{\bold{D=-31;D<0\checkmark}}}}}$

Conclusion→

After performing the calculation, we can see that the Discriminant thus obtained is -31, which is less that zero. So we can conclude that the roots are imaginary and no real roots exists.

Nature Of Roots:-

Roots are imaginary in nature $\checkmark$

HOPE IT HELPS.