Question

Form the quadratic equation if one of the roots of the quadratic equation is (a )4-3root2​

Answer 1

Answer:

x² - 8x - 2 = 0

Step-by-step explanation:

The quadratic equation will be of form ax² + bx + c = 0

if one root is 4 - 3√2.

=> x = 4 - 3√2

=> (x - 4) = - 3√2

squaring on both sides,

=> (x - 4)² = (- 3√2)²

=> x² - 8x + 16 = 18

=> x² - 8x + 16 - 18 = 0

=> x² - 8x - 2 = 0

Answer 2

Answer:

Case 1. No information about the co-efficient is given.

If only one root of the quadratic equation is given and there is no information about co-efficients of the equation, then it is not possible to find out the equation. It is because we always need two roots to form a quadratic equation and it is not possible to find the second root without any other data given. The other root can be any number and the equation will be different for each of this different roots.

Case 2. Co-efficients of the quadratic equation are rational.

Theorem

If p + √q is a root of the quadratic equation ax² + bx + c = 0 such that p, q, a, b, c ∈ ℚ(set of rational numbers), then p - √q is also a root of the quadratic equation.

According to this theorem if the co- effecients are rational and α = 4 - 3√2 is a root of the equation then β = 4 + 3√2 is the other root of the equation.

Now

α + β = 4 - 3√2 + 4 + 3√2 = 8

αβ = (4 - 3√2)(4 + 3√2) = 16-18 = -2

Hence the equation is

x² - (α + β)x + αβ = 0

or x² - 8x - 2 = 0

I hope you understand what I am trying to convey.