If the roots of nbsp-equation x-2 - 4x - c - 0 are real nbsp-then nbsp-c - 4-False-True-

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Standard X

Mathematics

Nature of Roots Using Discriminant

If the roots ...

Question

If the roots of equation $x^{2} + 4 x + c = 0$ are real then $c \geq 4$ .

True

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False

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Solution

The correct option is B
False

Given, $x^{2} + 4 x + c = 0$

Value of discriminant, $Δ = b^{2} - 4 a c = 4^{2} - 4 c = 16 - 4 c$

The roots of quadratic equation are real then $Δ \geq 0 16 - 4 c \geq 0 - 4 c \geq - 16 4 c \leq 16$
(The inequality changes when the equation is multiplied by $^{'} -^{v e}^{'}$

$∴ c \leq 4$

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If the roots of equation x2+4x+c=0 are real then c≥4.

The correct option is B False Given, x2+4x+c=0 Value of discriminant, Δ=b2−4ac=42–4c=16−4c The roots of quadratic equation are real then Δ≥016–4c≥0−4c≥−164c≤16 (The inequality changes when the equation is multiplied by ′−ve ′ ∴c≤4

If the roots of equation $x^{2} + 4 x + c = 0$ are real then $c \geq 4$ .