Question

3x²-x-24=0
solve this quadratic equation..​

Answer 1

Given :-

$3x {}^{2} - x - 24 = 0$

What to find out =Roots of the equation?

Solution :-

Factorise by splitting middle term

$3 {x}^{2} - x - 24 = 0 \\ \\ 3 {x}^{2} - 9x + 8x - 24 = 0 \\ \\ 3x(x - 3) + 8(x - 3) = 0 \\ \\ (x - 3)(3x + 8) = 0$

Now split it into possible cases

$(x - 3) = 0 \\ \\ \\ (3x + 8) = 0$

Hence,

$x_1 = (3 )\\ \\ x_</p><p>2 = ( - \frac{ 8}{3} )</p><p>$

Extra information :-

• A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable.

Answer 2

${\red{\underline{\underline{\bold{Given:-}}}}}$

• 3x²-x-24=0

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The roots of the equation ( the Value of x)

${\green{\underline{\underline{\bold{Solution:-}}}}}$

3x²-x-24=0

By splitting the middle term

$\implies$ 3x²-9x+ 8x -24=0

$\implies$ 3x(x - 3) + 8 ( x - 3) = 0

$\implies$ (3x+8)(x - 3) = 0

Now,Spilt the both terms

3x + 8 = 0 (or) x - 3 = 0

Hence,

x = $\frac{-8}{3}$

x = 3