Write the discriminant of $x^{2} + 5 x + 5 = 0$

Open in App

Solution

We know that a discriminant is an index to indicate whether the quadratic function has no intersection $(D < 0)$ , intersect as single point $(D = 0)$ or intersect at multiple roots $(D > 0)$ with the horizontal axis. Discriminant of a quadratic equation $a x^{2} + b x + c = 0$ is $D = b^{2} - 4 a c$ .

In the given quadratic equation $x^{2} + 5 x + 5 = 0$ , $a = 1, b = 5$ and $c = 5$ , therefore, the discriminant is:

$D = b^{2} - 4 a c = (5)^{2} - (4 \times 1 \times 5) = 25 - 20 = 5$

Hence, the discriminant is $5$ .

Suggest Corrections

Similar questions

Find the discriminant of the quadratic equation $x^{2}$ + 5 x – 3 = 0

Q. Write the discriminant of the following quadratic equations:

(i) 2x² − 5x + 3 = 0
(ii) x² + 2x + 4 = 0
(iii) (x − 1) (2x − 1) = 0
(iv) x² − 2x + k = 0, k ∈ R
(v)

\sqrt{3} x^{2} + 2 \sqrt{2} x - 2 \sqrt{3} = 0

(vi) x² − x + 1 = 0

Write the discriminant of the following quadratic equations:
(i) $2 x^{2} - 5 x + 3 = 0$ (ii) $x^{2} + 2 x + 4 = 0$
(iii) $(x - 1) (2 x - 1) = 0$ (iv) $x^{2} - 2 x + k = 0, k ϵ R$
(v) $\sqrt{3} x^{2} + 2 \sqrt{2} x - 2 \sqrt{3} = 0$ (vi) $x^{2} - x + 1 = 0$

Write the discriminant of the following equation :

x^{2} - 4 x + 2 = 0

Q. Find the discriminant of the following quadratic equations and discuss the nature of the roots .
1.

6 x^{2} - 13 x + 6 = 0

\sqrt{6} x^{2} - 5 x + \sqrt{6} = 0

24 x^{2} - 17 x + 3 = 0

x^{2} + 2 x + 4 = 0

x^{2} + x + 1 = 0

x^{2} - 3 \sqrt{3} x - 30 = 0

Join BYJU'S Learning Program

Write the discriminant of x2+5x+5=0

Write the discriminant of $x^{2} + 5 x + 5 = 0$