Question

Find the values of k for which the given equation has real and equal roots.

x

2 – 2x(1 + 3k) + 7(3 + 2k) = 0,by quadratic formula​

Answer 1

Answer:

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Step-by-step explanation:

we have given equation is

x² + 2x(1 + 3k) +7(3 + 2k) = 0

or

x² + 2(1 + 3k)x +7(3 + 2k) = 0

roots are equal

we have to find the value of k =?

now

we know that an equation have equal roots if and only if D = 0

=> b² -4ac = 0

here comparing the equation with

ax² + bx + c = 0

here

a= 1, b = 2(1 + 3k) and c= 7(3 + 2k)

now

b² - 4ac = 0

= [ 2(1 + 3k) ]² - 4 ×1×7(3 + 2k) = 0

= 4×(1 + 3k)² - 4×7(3 + 2k) = 0

= 4(1 + 9k² + 6k) - 4(21 +14k) =0

= (1 + 9k² + 6k) - (21 +14k) =0

=> 9k² - 8k -20 = 0

now solving the equation we get

= 9k² - 18k + 10k - 20 = 0

= 9k( k- 2) + 10(k -2) =0

=> 9k +10=0 and k -2 = 0

=> k = -10/9 and 2 answer