Question

solve by factorisation
4x2+40=31x​

Answer 1

• Either the given Equation is wrong, or it can't be solved by factorisation method.
• So, Quadratic Formula is applied here.
• Quadratic Formula has to be studied in Class X if you're a student of CBSE.

Here,

$\boxed{ \sf {4x}^{2} - 31x + 40 = 0} \\ \overbrace{ \text{ \: is of the form ax²+bx+c=0 \: }}\\ \\ \sf \underbrace{ \overline{ \: \: Discriminant = {b}^{2} - 4ac \: \: }}\\ = > {( - 31)}^{2} - 4(4)(40) \\ = > 961 - 640 \: \: = 321$

Now,

$\rm{}x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \: \: \: \: or \: \: \: \frac{ - b \pm \sqrt{ D} }{2a}\\ \\ \\ = > \frac{ - ( - 31) \pm \sqrt{321} }{2(4)} \\ \\ = > \frac{31 \pm \sqrt{321} }{8}$

So, Factors of 4x² + 40 = 31x are

$\tt\bigg(x - \frac{31 + \sqrt{321} }{8} \bigg)\bigg(x - \frac{31 - \sqrt{321} }{8} \bigg)$