Solve the following equation using the quadra | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given quadratic equation is $x^{2} + 6x + 5 = 0$.Comparing this with the standard form $ax^{2} + bx + c = 0$,we get $a = 1$,$b = 6$,and $c = 5

Vedclass · Accepted Answer

$-5, -1$

Vedclass · Answer

(A) The given quadratic equation is $x^{2} + 6x + 5 = 0$.Comparing this with the standard form $ax^{2} + bx + c = 0$,we get $a = 1$,$b = 6$,and $c = 5$.The quadratic formula is $x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$.First,calculate the discriminant $D = b^{2} - 4ac = (6)^{2} - 4(1)(5) = 36 - 20 = 16$.Since $D > 0$,real solutions exist.Substituting the values into the formula: $x = \frac{-6 \pm \sqrt{16}}{2(1)} = \frac{-6 \pm 4}{2}$.For the positive sign: $x = \frac{-6 + 4}{2} = \frac{-2}{2} = -1$.For the negative sign: $x = \frac{-6 - 4}{2} = \frac{-10}{2} = -5$.Thus,the solutions are $-5$ and $-1$.

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $x^{2}+6x+5=0$.

Similar Questions

Obtain the roots of the following equation using the method of 'completing the square': $3y^{2} + 7y - 20 = 0$.

The length of a rectangular garden exceeds its breadth by $6 \, m$. If the area of the garden is $216 \, m^2$,find the length and the breadth of the garden.

If one of the roots of $x^{2}-2x-c=0$ is $5$,the other root is ...........

If the roots of the following quadratic equation exist,find them by the method of completing the square: $3x^2 + 7x + 5 = 0$.

Solve the following equation using the method of factorization and write its solution set: $x + 2 - \frac{6}{x + 2} = 1$

Vedclass Test Series

Exam Paper Generator

Online Exam Module