Question

find the ratio of sum and product of the roots of the equation 7 x squared - 12 x + 18 = 0
solve this quadratic equation

Answer 1

Solution :

Compare 7x² - 12x + 18 = 0 with

ax² + bx + c = 0 , we get

a = 7 , b = -12 , c = 18

i ) Sum of the roots = -b/a

= -(-12)/7

= 12/7

ii ) Product of the roots = c/a

= 18/7

iii ) ratio of sum and product of

the roots = ( 12/7 )/(18/7)

= 12/18

= 2:3

iv ) 7x² - 12x + 18 = 0

Discreminant (D) = b² - 4ac

= (-12)² - 4×7×18

= 144 - 504

= -360

By Quadratic Formula ,

x = [ -b ± √D ]/(2a)

= [ -(-12) ± √-360 ]/(2×7) ]

= [12± 6√(-10)]/14

= [ 6±3√(-10)]/7

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