Algebraic Expressions, Identities and Equations

IMPORTANT

Algebraic Expressions, Identities and Equations: Overview

This topic covers concepts, such as, Relationship between Zeros and Coefficients of a Quadratic Polynomial, Formation of Quadratic Polynomial with Given Zeros, Geometrical Meaning of the Zeros of a Polynomial & Theorems of Polynomial etc.

Important Questions on Algebraic Expressions, Identities and Equations

EASY
IMPORTANT

If x+1x=5, then the value of x8+1x8 is:

MEDIUM
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If p=101, then find the value of pp2-3p+3-13.

EASY
IMPORTANT

If 4x3+2p=10 for what value of p, x=12?

MEDIUM
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If 1x+1+ 2y+2 +1009z+1009 =1, then find the value of  xx+1+yy+2+zz+1009=?

MEDIUM
IMPORTANT

What should come in the place of (?) for the expression given below?

(y-z)3+(z-x)3+(x-y)3=?

MEDIUM
IMPORTANT

Find the value of the followings

1+1x1+1x+11+1x+21+1x+3

EASY
IMPORTANT

The numerical coefficient of y in the expression 2x+3y+7z is:

MEDIUM
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If x+ax =b , then find the value of x2+bx+a bx2-x3

EASY
IMPORTANT

A number when divided by 91 gives a remainder17 . When the same number is divided by13, the remainder will be-

MEDIUM
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If a+1a=3, find the value of a3+(1a)3=?

EASY
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The value of 1+1a1+1a+11+1a+21+1a+31+1a+4 _____.

EASY
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If a×b=a+b+ab then the value of 12×4 is :

EASY
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Find the value of k, if x-1 is a factor of 4x3+3x2-4x+k.

EASY
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If, x= 3+22 , what is the value of x2+1x2?

HARD
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If $$\left( { x }^{ 2 }+\cfrac { 1 }{ { 5 } } x+{ a }^{ 2 } \right) $$ is a perfect square, then a is -

EASY
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If a(a + 2) = a + b + c, b(b + 2) = a + b + c and c(c+2)=a+b+c, then what is the value of 1a+2+1b+2+1c+2?

MEDIUM
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If x = 3 +22 ,then the value of x4+1x4{ x }^{ 4 }+\cfrac { 1 }{ { x }^{ 4 } } is

MEDIUM
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In a division sum, the divisor is 4 times the quotient and twice the remainder. If a and b are respectively the divisor and the dividend then

MEDIUM
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1+m2x2+2 mcx+c2-a2=0 has equal roots if ________.