Question

show that each of the following equations has, real roots , and solve each by using the quadratic formula: 6-x-x^2=0​

Answer 1

Answer:

The discriminant

= b2 – 4ac

= 49 – 4 × 6 × 2

= 1 > 0

So, the given equation has two distinct real roots.

Now, 6x2 – 7x + 2 = 0 i.e.,

36x2 – 42x + 12 = 0

i.e., 6x - (7/2)2 + 12 - 49/4 = 0

i.e., 6x - (7/2)2 - (1/2)2

= 0 or (6x - 7/2)2 = (1/2)2

The roots are given by

6x - 7/2 = ±1/2

i.e., 6x = 4, 3

i.e., x = 2/3, 1/2.

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Answer 2

Answer:

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