Question

1. Fill in the blanks:-
(a) If the quadratic equation x2 - 2x + k = 0 has equal roots, then value of k is .....
(b) If the product of the roots of the equation x2 - 3x + k = 0 is - 2 then the value of k is
(c) If the sum of the roots of a quadratic equation is 6 and their product is 6, then the equation is
(d) The ratio of the sum and product of the roots of the equation 7x2 - 12x + 18 is ....
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Answer 1

Answer:

a) 1 , b) -2 , c) x2 - 6x + 6 =0 , d) 2/3

Answer 2

a) 1

x²- 2x + k = 0 has equal roots .

Let both the roots be y

Sum of roots = 2y = 2

=> y = 1

Product of roots = y² = k

=> k = 1

b) -2

x² - 3x + k = 0 has product of roots equal to -2

So , the value of k= -2

c) x²- 6x + 6

Sum of roots = 6

Product of roots = 6

Quatratic equation -

=> x² - (sum of roots)x + product of roots

=> x² -6x +6

d) 2/3

7x²- 12x + 18

Ratio = sum of roots / product of roots

=> (12/7)/(18/7)

=> 2/3