Find the nature of the roots of the quadratic equation 3x²+5kx+16=0 has real and equal roots.
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Answer:
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Step-by-step explanation:
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Answer:
Value of k is ± 2.77.
Step-by-step explanation:
Given equation is 3x² + 5kx + 16 = 0
Comparing with ax² + bx + c = 0,
- a = 3
- b = 5k
- c = 16
Given that, roots are real and equal
b² - 4ac = 0
=> (5k)² - 4 * 3 * 16 = 0
=> 25k² - 12 * 16 = 0
=> 25k² - 192 = 0
=> 25k² = 192
=> k² = 192/25
=> k² = 7.68
=> k = ± √7.68
=> k = ± 2.77
So,
Value of k is ± 2.77.
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