Question

x²-7x+2=0 and alpha, beta are the two roots then find ​

Answer 1

CORRECT QUESTION:

If α & β are the roots of the quadratic equation x² - 7x + 2 = 0. then find the roots.

ANSWER:

Given, quadratic equation

x² - 7x + 2 = 0

To find the roots we need to factorise of simplify with quadratic equation formula

Note:

• We can't solve this problem using factorisation
• Because, the middle term ( 7 ) is a prime

Quadratic equation formula

${ \rm{ x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }}$

Here,

a = 1 , b = -7 , c = 2

$\to{ \sf{x = \frac{ - ( - 7) \pm \sqrt{ {( - 7) }^{2} - 4(1)(2) } }{2(1)} }}$

$\to{ \sf{x = \frac{7 \pm \sqrt{49 - 8} }{2} }}$

${ \sf{ \to x = \frac{7 + \sqrt{41} }{2}(or) \frac{7 - \sqrt{41} }{2} }}$

Now,

α = 7 + √41/2

β = 7 - √41/2

Hence, α = 7 + √41/2 , β = 7 - √41/2

Answer 2

Answer:

α = 7 + √41/2

β = 7 - √41/2