Find the value of -
$(x^{2} - 3 x + 5) + (2 x^{2} - x - 2) - (3 x^{2} + 7 x - 3)$

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Solution

$(x^{2} - 3 x + 5) + (2 x^{2} - x - 2) - (3 x^{2} + 7 x - 3)$
$= x^{2} - 3 x + 5 + 2 x^{2} - x - 2 - 3 x^{2} - 7 x + 3$
$= 3 x^{2} - 3 x^{2} - 11 x + 6$
$= - 11 x + 6$
$∴ (x^{2} - 3 x + 5) + (2 x^{2} - x - 2) - (3 x^{2} + 7 x - 3) = - 11 x + 6$

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Question 3
Which of the following equations has 2 as a root?
(a) $x^{2} - 4 x + 5 = 0$
(b) $x^{2} + 3 x - 12 = 0$
(c) $2 x^{2} - 7 x + 6 = 0$
(d) $3 x^{2} - 6 x - 2 = 0$

Q. Find the nature of the roots of the following quadratic equation:

3 x^{2} + 7 x + 2 = 0

{(x + 3)}^{2} + 4 x + 7 = 0

2 x^{2} - 8 x + 34 = 0

x^{2} + 2 \sqrt{3 x} - 1 = 0

Question 3
Which of the following equations has 2 as a root?
(a) $x^{2} - 4 x + 5 = 0$
(b) $x^{2} + 3 x - 12 = 0$
(c) $2 x^{2} - 7 x + 6 = 0$
(d) $3 x^{2} - 6 x - 2 = 0$

Solve for the value of $x$ : $\sqrt{{3 x}^{2} - 7 x - 30} - \sqrt{{2 x}^{2} - 7 x - 5} = x - 5$

Q. Match the following.

	Column - I		Column - II
(P)	$(x^{2} + 5) (x^{3} + 3) + 5$	(1)	${- x}^{3} - 3 x^{2} + 3 x + 2$
(Q)	$(\frac{- 10}{3} x y^{3}) \times (\frac{6}{5} x^{3} y)$	(2)	$- x^{3} + x^{2} + 3 x - 6$
(R)	$(x^{3} - x^{2} - x - 2) - (2 x^{3} + 2 x^{2} - 4 x - 4)$	(3)	$x^{5} + 5 x^{3} + 3 x^{2} + 20$
(S)	$(x^{3} - x^{2} - x - 2) + (2 x^{2} - 2 x^{3} + 4 x - 4)$	(4)	$- 4 x^{4} y^{4}$

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Find the value of -(x2−3x+5)+(2x2−x−2)−(3x2+7x−3)

(x2−3x+5)+(2x2−x−2)−(3x2+7x−3)=x2−3x+5+2x2−x−2−3x2−7x+3=3x2−3x2−11x+6=−11x+6∴(x2−3x+5)+(2x2−x−2)−(3x2+7x−3)=−11x+6

Find the value of -
$(x^{2} - 3 x + 5) + (2 x^{2} - x - 2) - (3 x^{2} + 7 x - 3)$

$(x^{2} - 3 x + 5) + (2 x^{2} - x - 2) - (3 x^{2} + 7 x - 3)$
$= x^{2} - 3 x + 5 + 2 x^{2} - x - 2 - 3 x^{2} - 7 x + 3$
$= 3 x^{2} - 3 x^{2} - 11 x + 6$
$= - 11 x + 6$
$∴ (x^{2} - 3 x + 5) + (2 x^{2} - x - 2) - (3 x^{2} + 7 x - 3) = - 11 x + 6$