Question 83 (xxi)

Multiply the following:

$(3 x^{2} + 4 x - 8), (2 x^{2} - 4 x + 3)$

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Solution

We have, $(3 x^{2} + 4 x - 8)$ and $2 x^{2} - 4 x + 3$
$∴ (3 x^{2} + 4 x - 8) (2 x^{2} - 4 x + 3) = 3 x^{2} (2 x^{2} - 4 x + 3) + 4 x (2 x^{2} - 4 x + 3) - 8 (2 x^{2} - 4 x + 3) = 6 x^{4} - 12 x^{3} + 9 x^{2} + 8 x^{3} - 16 x^{2} + 12 x - 16 x^{2} + 32 x - 24$
$= 6 x^{4} - 12 x^{3} + 8 x^{3} + 9 x^{2} - 16 x^{2} - 16 x^{2} + 12 x + 32 x - 24$ [grouping like terms]
$= 6 x^{4} - 4 x^{3} - 23 x^{2} + 44 x - 24$

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Question 83 (xviii)

Multiply the following :

$(\frac{3}{4} x - \frac{4}{3} y), (\frac{2}{3} x + \frac{3}{2} y)$

Question 83 (xviii)

Multiply the following :

$(\frac{3}{4} x - \frac{4}{3} y), (\frac{2}{3} x + \frac{3}{2} y)$

Question 10
Which of the following equations has no real roots?
(A) $x^{2} - 4 x + 3 \sqrt{2} = 0$
(B) $x^{2} + 4 x - 3 \sqrt{2} = 0$
(C) $x^{2} - 4 x - 3 \sqrt{2} = 0$
(D) $3 x^{2} - 4 \sqrt{3} x + 4 = 0$

Q. Solve the following equations:

3 x^{2} - 4 x + \sqrt{3 x^{2} - 4 x - 6} = 18

(7 - 4 \sqrt{3})^{x^{2} - 4 x + 3} + (7 + 4 \sqrt{3})^{x^{2} - 4 x + 3} = 14

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Algebraic Identities

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Question 83 (xxi) Multiply the following: (3x2+4x−8),(2x2−4x+3)

We have, (3x2+4x−8) and 2x2−4x+3 ∴(3x2+4x−8)(2x2−4x+3)=3x2(2x2−4x+3)+4x(2x2−4x+3)−8(2x2−4x+3)=6x4−12x3+9x2+8x3−16x2+12x−16x2+32x−24 =6x4−12x3+8x3+9x2−16x2−16x2+12x+32x−24 [grouping like terms] =6x4−4x3−23x2+44x−24

Question 83 (xxi)

Multiply the following:

$(3 x^{2} + 4 x - 8), (2 x^{2} - 4 x + 3)$