Question

4) Form a quadratic equation if the roots of the quadratic equation are 2 +
✓7 and 2 - V7​

Answer 1

Answer:

x²-4x-3 = 0

Explanation:

Let the equation be ax²+bx+c = 0

The rules of quadratic equation say that,

Sum of roots = -b/a

Sum of roots = -b/aProduct of roots = c/a

Sum = (2 + √7) + (2 - √7) = 4 = -b/a => b = -4a

Product = (2 + √7)(2 - √7) = 4 - 7 = -3 = c/a => c = -3a

So, the equation becomes, ax²-4ax-3a = 0, a is any constant.

that is, a × (x²-4x-3) = 0

So, the required equation is x²-4x-3 = 0

Please vote if found helpful :)