The equation x 2-4 x - c -0 has real roots- thenA- C - 4B- C - 4C- c - 6D- c - 8

The correct option is B c ≤ 4 For nbsp;x^2 + 4x + c = 0, value of discriminant, D = 4^2 – (4× 1× c )= 16 4c It is given that the roots of the given quadrati ...

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Standard X

Mathematics

Nature of Roots of a Quadratic Equation

The equation ...

Question

The equation $x^{2} + 4 x + c = 0$ has real roots, then

$c \geq 4$

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$c \leq 4$

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$c \leq 8$

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$c \geq 6$

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Solution

The correct option is B
$c \leq 4$

For $x^{2} + 4 x + c = 0$ , value of discriminant, $D = 4^{2} - (4 \times 1 \times c) = 16 - 4 c$

It is given that the roots of the given quadratic equation are real.

$\Rightarrow D \geq 0$

$\Rightarrow 16 - 4 c \geq 0$

$\Rightarrow 16 \geq 4 c$

$\Rightarrow c \leq 4$

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The equation x2+4x+c=0 has real roots, then

The correct option is B c≤4 For x2+4x+c=0, value of discriminant, D=42–(4×1×c)=16−4c It is given that the roots of the given quadratic equation are real. ⇒D≥0 ⇒16–4c≥0 ⇒16≥4c ⇒c≤4

The equation $x^{2} + 4 x + c = 0$ has real roots, then