Question

`4x2 + x - 3`


​

Answer 1

`\boxed{\textsf{ The roots of the quadratic equation is \textbf{ (-4) and 3 }.}}`

Explanation:

A quadratic equation is given to us . Here we aren't given what to do with it. So , lets find out the roots of the equation . The given quadratic equation is :-

`\sf\implies 4x^2+x-3 =0`

Now with respect to Standard form ax²+bx + c . The roots of the equation can be find out by the quadratic formula also known as " Shreedharyacharya's Formula " .

Quadratic Formula :-

`\boxed{\boxed{\sf x =(-b\pm √(b^2-4ac))/(2a)}}`

Now with respect to Standard Form we have ,

• a = 4 •b = 1 •c = (-3)

Put on the respective values :-

`\sf\implies x = (-b\pm √(b^2-4ac))/(2a) \\\\\sf\implies x =(-1\pm√(1^2-4(1)(-3)))/(2(1))\\\\\sf\implies x =(-1\pm √(1+48))/(2)\\\\\sf\implies x =(-1\pm √(49))/(2)\\\\\sf\implies x = (-1\pm 7 )/(2)\\\\\sf\implies x =(-1-7)/(2),(-1+7)/(2)\\\\\sf\implies x =(-8)/(2),(6)/(2)\\\\\sf\implies \boxed{\pink{\sf x = (-4) , 3 }}`