Question

Q. 1 If both x-2 and x-1/2 are factors of ax² +5x+c show that. a= c
Q. 2 find the value of A and B if 5+2√3/7+4√3=a+b√3.​

Answer 1

(1) Given, f(x) = px^2+5x+r and factors are x-2, x-1/2

Substitute x = 2 in place of equation, we get

= p*2^2+5*2+r=0

= 4p + 10 + r = 0 ------------ (i)

Substitute x = 1/2 in place of equation.

p/4 + 5/2 + r = 0

p + 10 + 4r = 0 ------------------- (ii)

On solving (i),(ii) we get

4p+r=-10 and p+4r+10=0

4p+r=p+4r

3p=3r

p = r.

(2) Lhs = (5+2√3)/(7+4√3)

= [(5+2√3)(7-4√3)]/[(7-4√3)(7+4√3)]

=[35-20√3+14√3-24]/[7²-(4√3)²]

=[11-6√3]/[49-48]

=11-6√3

therefore

11-6√3 = a+b√3

compare both sides

a= 11, b= -6

Hope this helps!