Q.

Statement 1: If 27a+9b+3c+d=0, then the equation f(x)=4ax3+3bx2+2cx+d=0. Has at least one real root lying between (0, 3).
Statements 2: If f(x) is continuous in [a, b], derivable in (a, b) such that f(a) = f(b), then at least one
point c(a,b) such that f(c)=0.

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a

If both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT - 1

b

If STATEMENT – 1 is TRUE and STATEMENT 2 is FALSE

c

If STATEMENT – 1 is FALSE and STATEMENT 2 is TRUE

d

If both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT – 1

answer is A.

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Detailed Solution

Consider f(x)=4ax3+3bx2+2cx+d=0
f(x)=ax4+bx3+cx2+dx+ef(0)=f((3)
Hence, Rolle’s theorem is applicable for f(x), there
exists at least one c in (a,b) such that f(c)=0..

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Statement 1: If 27a+9b+3c+d=0, then the equation f(x)=4ax3+3bx2+2cx+d=0. Has at least one real root lying between (0, 3).Statements 2: If f(x) is continuous in [a, b], derivable in (a, b) such that f(a) = f(b), then at least onepoint c∈(a,b) such that f(c)=0.