The minimum value of the expression $4 x^{2} + 2 x + 1$ is-

1

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\frac{1}{3}

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\frac{1}{2}

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\frac{3}{4}

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Solution

The correct option is D $\frac{3}{4}$
For a general quadratic equation ${a x}^{2} + b x + c = 0, w h e r e a > 0 t h e m i n i m u m v a l u e o f e x p r e s s i o n o c c u r s a t \frac{- D}{4 a} ∴ {4 x}^{2} + 2 x + 1 m i n i m u m v a l u e = \frac{- (2^{2} - 4.4.1)}{4.4} = \frac{12}{16} = \frac{3}{4}$

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The minimum value of the expression 4x2+2x+1 is-

The correct option is D 34For a general quadratic equation ax2+bx+c=0,wherea>0theminimumvalueofexpressionoccursat−D4a∴4x2+2x+1minimumvalue=−(22−4.4.1)4.4=1216=34

The minimum value of the expression $4 x^{2} + 2 x + 1$ is-