If a gt-0 and the equation ax-2-bx-c-0 has two real roots - and - such that- - - - 1- - - - - 1- then - a-b-c - 0a-b-c - 0a- - b -c - 0a-c - 0

The correct options are A a+b+c ≥ 0 B a b+c ≥ 0 C a+ | b |+c ≥ 0 D a c ≥ 0 As both the roots lie in the interval [ 1,1], we have y( 1) ≥ 0, y(1) ≥ 0 ⇒ a b+c ...

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Byju's Answer

Standard X

Mathematics

Inequalities involving modulus function

If a gt;0 a...

Question

If a>0 and the equation $a x^{2} + b x + c = 0$ has two real roots $α$ and $β$ such that $| α | \leq 1, | β | \leq 1,$ then

a + b + c \geq 0

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a - b + c \geq 0

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a + | b | + c \geq 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

a - c \geq 0

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Solution

The correct options are
A $a + b + c \geq 0$
B $a - b + c \geq 0$
C $a + | b | + c \geq 0$
D $a - c \geq 0$
As both the roots lie in the interval [-1,1], we have
$y (- 1) \geq 0, y (1) \geq 0 \Rightarrow a - b + c \geq 0, a + b + c \geq 0 \Rightarrow a + | b | + c \geq 0 A l s o, α β \leq | α β | = | α | | β | \leq 1 \Rightarrow \frac{c}{a} \leq 1 o r c \leq a o r a - c \geq 0$

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