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Solving a Quadratic Equation by Completion of Squares Method

Find the prod...

Question

Find the products:
(a) $(4 x - 5) (2 x^{2} - 7 x - 3)$
(b) $(x^{2} - 5) (x^{3} - 2 x^{2} + 4 x + 3)$

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Solution

(a) $(4 x - 5) (2 x^{2} - 7 x - 7)$
$= 8 x^{3} - 28 x^{2} - 28 x - 10 x^{2} + 35 x + 35$
$= 8 x^{3} - 38 x^{2} + 7 x + 35$

(b) $(x^{2} - 5) (x^{3} - 2 x^{2} + 4 x + 3)$
$= x^{5} - 2 x^{4} + 4 x^{3} + 3 x^{2} - 5 x^{3} + 10 x^{2} - 20 x - 15$
$= x^{5} - 2 x^{4} - x^{3} + 13 x^{2} - 20 x - 15$

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Find the domain of $f(x)=\sqrt (x2+4x−2x2−3)$f(x)=x2+4x−2x2−3

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)	$- 4 x^{4} y^{4}$

Q. Find the value of the following limit:

lim x \to \infty \frac{2 x^{2} + 7 x - 2}{6 x^{3} - 4 x + 3}

Solve: $(4 x^{4} - 5 x^{3} - 7 x + 1) \div (4 x - 1)$ .

(4 x^{4} - {5 x}^{3} - 7 x + 1) \div (4 x - 1)

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