Question

7. If arithmetic mean of two numbers a and b is 8 and ab = 9, find a quadratic equation whose roots are a and b.
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Answer 1

Answer :-

Given :-

• Arithmetic mean of a and b = 8
• ab = 9

To Find :-

• Quadratic equation whose zeros are a and b.

Solution :-

Arithmetic mean of a and b = 8

→ ( a + b ) / 2 = 8

→ a + b = 16

Now, we have -

→ Sum of roots of quadratic equation ( a + b ) = 16

→ Product of roots ( ab ) = 9

Also, we know that -

→ Sum of roots = -b / a

→ Product of roots = c / a

So,

→ -b / a = 16

→ c / a = 9

Assuming a to be 1 :-

→ -b = 16 or b = -16

→ c = 9

Hence,

Quadratic equation → ax² - 16x + 9 = 0