Question

write the nature of the roots of 4x square - 2x - 5=0
pls answer it fastly

Answer 1

here we have,
$b {}^{2} - 4ac \: = (- 2) {}^{2} - 4 \times 4 \times 5 \\ = 4 - 80 \\ = - 76 \\ which \: is \: smaller \: than \: zero \: \\ therefore \: equation \: has \: no \\ \: real \: root$

Answer 2

We know that Nature of roots of Quadratic equation is dependent on discriminant.

(i) When D = 0, then the roots are real and equal.

(ii) When D < 0, then the roots are imaginary and unequal.

(iii) When D > 0, then the roots are real and unequal.

Now,

Given Equation is 4x^2 - 2x - 5 = 0.

On comparing with ax^2 + bx + c = 0, We get a = 4, b = -2, c = -5.

We know that Discriminant D = b^2 - 4ac.

⇒ (-2)^2 - 4(4)(-5)

⇒ 4 + 80

⇒ 84.

Since, D > 0.

∴ The nature of roots are real and unequal.

Hope it helps!