Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 45

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Let $x_{1}, x_{2}, x_{3}, x_{4}$ denote the four roots of the equation
$x^{4} + k x^{2} + 90 x - 2009 = 0$ . If $x_{1} x_{2} = 49$ , find the value of $k$ .

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Important Questions on Algebra

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 46

Let

x

be a real number such that

x^{2} - 15 x + 1 = 0

. Find the last two digits of

x^{4} + \frac{1}{x^{4}}

.

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 47

If

x, y

and

z

are real numbers such that

x + y + z = 9

and

x y + y z + z x = 24

, find the largest possible value of

z

.

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 51

If

a, b, c

and dare real numbers such that

\frac{b + c + d}{a} = \frac{a + c + d}{b} = \frac{a + b + d}{c} = \frac{a + b + c}{d} = r

, find the sum of all the possible values of

r .

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 55

Let

g (x) = x^{5} + x^{4} + x^{3} + x^{2} + x + 1

What is the remainder when the polynomial

g (x^{12})

is divided by the polynomial

g (x) ?

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 57

How many real numbers

x

satisfy the equation

3^{2 x + 2} - 3^{x + 3} - 3^{x} + 3 = 0 ?

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IMPORTANT

Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.2>Q 60

What is the sum of all the roots of the equation

\sqrt{5 |x| + 8} = \sqrt{x^{2} - 16}

?

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.3>Q 1

For what values of $b$ do the equations:

$1988 x^{2} + b x + 8891 = 0$ and $8891 x^{2} + b x + 1988 = 0$ have a common root?

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Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.3>Q 2

Given that the equation in $x$ has at least a real root, find the range of $m .$

$(m^{2} - 1) x^{2} - 2 (m + 2) x + 1 = 0$