Ans PL: 14 If (x-6) is a factor of x3+ax2+bx-b and a-b=7, find the value of a and - Maths - Quadratic Equations

Question

Ans PL:

14 If (x-6) is a factor of x3+ax2+bx-b and
a-b=7, find the value of a and b

15 Solve the following pair of linear equations for x and y:

x a + y b = 2 ,             a x - b y
= a 2 - b 2

16 Solve for x : 2 2 x + 3 x - 3 - 25 x - 3 2 x + 3 = 5

18 If an isosceles triangle ABC, in which AB=AC=6 cm is inscribed
in a circle of radius 9cm Find the area of the triangle

Varun Rawat · Accepted Answer

15

If the given equations are :a1x + b1y + c1 = 0  and  a2x + b2y + c2 = 0, then by cross- multiplication methodx = b1c2 - b2c1a1b2 - a2b1   ;  y = a1c2 - a2c1a1b2 - a2b1The given system of equations are :xa + yb = 2⇒bx + ay - 2ab = 0     
1ax - by - a2 - b2 = 0     
2Now, by cross multiplication :x = -aa2 - b2 - 2ab2-b2 - a2 ;  y = +ba2 - b2 - 2a2b-b2 - a2⇒x = -a3 - ab2-a2 + b2; y = -a2b - b3-a2 + b2⇒x = -aa2 + b2-a2 + b2; y = -ba2 + b2-a2 + b2⇒x = a; y = b

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