If the graph of $y = 3 x^{2} + 2 \sqrt{b} x + 5$ does not touch x-axis , which of the following is true?

b > 50

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b < 15

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b < 50

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b > 15

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Solution

The correct option is B
b < 15

Given $y = 3 x^{2} + 2 \sqrt{b} x + 5$

If D > 0 $\Rightarrow$ Graph touches x-axis at 2 points

D = 0 $\Rightarrow$ Graph touches x-axis at 1 point

D < 0 $\Rightarrow$ Graph don't touch x-axis

$D = b^{2} - 4 a c = {(2 \sqrt{b})}^{2} - 4 (3) (5)$ < 0

4b < 4(3)(5)

b < 15

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If the graph of y=3x2+2√bx+5 does not touch x-axis , which of the following is true?

The correct option is B b < 15 Given y=3x2+2√bx+5 If D > 0 ⇒ Graph touches x-axis at 2 points D = 0 ⇒ Graph touches x-axis at 1 point D < 0 ⇒ Graph don't touch x-axis D=b2−4ac=(2√b)2−4(3)(5) < 0 4b < 4(3)(5) b < 15

If the graph of $y = 3 x^{2} + 2 \sqrt{b} x + 5$ does not touch x-axis , which of the following is true?