Question

Solve the equation x2-5x-24=0

Answer 1

Answer:

The solution of the given quadratic equation is $x=-3,8$

Step-by-step explanation:

The given quadratic equation is $x^2-5x-24=0$

We shall solve it based on the formula of roots of a quadratic equation.

For a quadratic equation of the form $ax^2+bx+c=0$ the roots of the equation are given by the relation as follows

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

For the given equation,

$a=1,b=-5,c=-24$

Hence its roots are calculated as follows

$x=\frac{-(-5)\pm \sqrt{5^2-4(1)(-24)}}{2(1)}\\=\frac{5\pm11}{2}=\frac{16}{2}, \frac{-6}{2} \\= > x=-3,8$

Therefore,

The solution of the given quadratic equation is $x=-3,8$

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Answer 2

Answer:

8 and - 3 are the zeroes of the given quadratic equation.

Step-by-step explanation:

Explanation:

Given that, $x^2 - 5x - 24 = 0$

Quadratic equation - The polynomial equations of degree two in one variable of type f(x) = $ax^2$ + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations.

It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f(x).

Step 1:

We have $x^2 - 5x - 24 = 0$

We solve this quadratic equation by  middle term splitting method.

⇒ $x^2 - 8x + 3x - 24 = 0$

⇒ x(x - 8) + 3 (x - 8)= 0

⇒(x - 8)(x + 3) = 0

⇒x - 8 = 0 and x + 3 = 0

⇒ x = 8 and x = -3.

Final answer:

Hence, 8 and - 3 are the zeroes of the given quadratic equation.

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