Question

Alpha and beta are the roots of the equation x2-3x+1=0, then find roots of x2-7x+1=0

Answer 1

comparing the equation x² -7x +1 = 0 with ax² + bx + c = 0

we get, a= 1

b = -7

c = 1

alpha = - b / a. .... .......acc, to formula

= -(-7) / 1

= +7

alpha = 7

beta = c/a......acc, to formula

= 1/1

= 1

the roots of the equation x²-7x+1 =0 are 7 and 1

Answer 2

Hey

$x {}^{2} - 7x + 1 = 0 \\ \\ = > x {}^{2} - 7x = - 1 \\ \\ = > x {}^{2} - 2( \frac{14}{2} )x + ( \frac{14}{2} ) {}^{2} = - 1 + ( \frac{14}{2} ) {}^{2} \\ \\ = > (x - 7) {}^{2} = - 1 + 49 \\ \\ = > (x - 7) { }^{2} = 48 \\ \\ = > x - 7 = \sqrt{48 } \\ \\ = > x - 7 = -4 \sqrt{3} \: \: or \: \: 4 \sqrt{3 } \\ \\ = > x = 7 - 4 \sqrt{3} \: or \: 7 + 4 \sqrt{3}$

Btw, 14/2=7

I hope it helps you!!!