Question

28-.Find the nature of roots of the quadratic equation x² + x - 5 = 0.​

Answer 1

Answer:

For ax

2

+bx+c=0, the discriminant, Δ=b

2

−4ac.

(i) Here, a=1; b=-1 and c= -10.

Now, the discriminant is Δ=b

2

−4ac

=(−11)

2

−4(1)(−10)=121+40=161

Thus, Δ>0.

Therefore, the roots are real and unequal.

(ii) Here, a=4; b=-28 and c= 49.

Now, the discriminant is Δ=b

2

−4ac

=(−28)

2

−4(4)(49)=0

Since Δ=0 3= , the roots of the given equation are real and equal.

(iii) Here, a=2; b=5 and c= 5.

Now, the discriminant is Δ=b

2

−4ac

=(5)

2

−4(2)(5)

=25−40=−15

Since Δ<0, the equation has no real roots.

Answer 2

Answer:

The nature of the roots is real and distinct

Step-by-step explanation:

Let f(x) = x² + x - 5 = 0

let D be the discriminant

D = b² - 4ac

D = 1² - [4 * 1 * (-5)]

D = 1² + 20

D = 21

Since D > 0, the roots are real and distinct