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Standard XII

Mathematics

Relations between Roots and Coefficients : Higher Order Equations

Let a , b , c...

Question

Let $a, b, c, d$ be real positive numbers. Then the maximum number of roots of the equation $a | x |^{3} + b x^{2} + c | x | + d = 0$ is

6

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4

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2

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0

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Solution

The correct option is D $0$
Sum of four positive numbers cannot be zero.

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Similar questions

Q. Let

a, b, c

be three distinct positive real numbers, then the number of real roots of

a x^{2} + 2 b | x | + c = 0

Q. Let

a, b, c, d

be distinct real numbers such that

a, b

are roots of

x^{2} - 5 c x - 6 d = 0,

and

c, d

are roots of

x^{2} - 5 a x - 6 b = 0.

Then

b + d

Q. Let

a, b, c, d

be distinct real numbers and

a

and

b

are the roots of quadratic equation

x^{2} - 2 c x - 5 d = 0

. If

c

and

d

are the roots of the quadratic equation

x^{2} - 2 a x - 5 b = 0

.then find the numerical values of

a + b + c + d

Find the minimum value of a+b+c+d in the equation $x^{5} - a x^{4} + b x^{3} - c x^{2} + d x - 243 = 0,$ if it is given that the roots are positive real numbers ?

Let a and b be nonzero real roots of the quadratic equation x²+ ax + b = 0 and a + b, a -b and - a -b be the roots of the equation x⁴+ax³+cx²+dx+e=0. Then which of the following statement is false?

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Let a,b,c,d be real positive numbers. Then the maximum number of roots of the equation a|x|3+bx2+c|x|+d=0 is

The correct option is D 0Sum of four positive numbers cannot be zero.

Let $a, b, c, d$ be real positive numbers. Then the maximum number of roots of the equation $a | x |^{3} + b x^{2} + c | x | + d = 0$ is

The correct option is D $0$
Sum of four positive numbers cannot be zero.