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$Let a, b, c, d are non - zero real numbers such that 6 a + 4 b + 3 c + 3 d = 0, then the equation$ $a x^{3} + b x^{2} + c x + d = 0 has$

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at least are root in [−2,0]

at least one root in 0,2

at least one root in [-2,2]

no root in [−2,2]

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Correct option is B

We have ax3+bx2+cx+d=0 Let f(x)=ax44+bx33+cx22+dx+e∴f(0)=ef(2)=4a+8b3+2c+2d+e=(12a+8b+6c+6d)3+e=23(6a+4b+3c+3d)+e=0⇒f(2)=e∴ By Rolle's theorem, there exist at least one value of x∈(0,2) such that f′(x)=0

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Let a,b,c,d are non − zero real numbers such that 6a+4b+3c+3d=0, then the equation ax3+bx2+cx+d=0 has

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$Let a, b, c, d are non - zero real numbers such that 6 a + 4 b + 3 c + 3 d = 0, then the equation$ $a x^{3} + b x^{2} + c x + d = 0 has$