Question

Factorise 3x^2-x-4 using splitting the middle term.

Answer 1

Given :

$3 {x}^{2} - x - 4 = 0$

What to find out = Roots of the equation?

Solution :

Factorise by splitting middle term

$3 {x}^{2} - x - 4 = 0 \\ 3 {x}^{2} - 4x + 3x - 4 = 0 \\ x(3x - 4) + 1(3x - 4) = 0 \\ (3x - 4)(x + 1) = 0$

Hence

$x_1 = \frac{4}{3} \\ x_2 = - 1$

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

✯✯ QUESTION ✯✯

Factorise ${3x}^{2}-x-4$ using splitting the middle term.

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✰✰ ANSWER ✰✰

$\longmapsto\tt{{3x}^{2}-x-4}$

$\longmapsto\tt{{3x}^{2}-(4x-3x)-4}$

$\longmapsto\tt{{3x}^{2}-4x+3x-4}$

$\longmapsto\tt{x(3x-4)+1(3x-4)}$

$\longmapsto\tt{(x+1)(3x-4)}$

➜Now ,

$\longmapsto\tt{x+1=0}$

$\green\longmapsto\:\large\underline{\boxed{\bf\purple{x}\orange{=}\red{-1}}}$

$\longmapsto\tt{3x-4=0}$

$\longmapsto\tt{3x=4}$

$\purple\longmapsto\:\large\underline{\boxed{\bf\orange{x}\pink{=}\green{\dfrac{4}{3}}}}$