Question

If the three equations
X^2 + ax + 12 = 0, x^2 + bx + 15 = 0 and
x^2 + (a + b)x+ 36 = 0 have a common positive root,
find a and b and the roots of the equations.​

Answer 1

Answer:

x=3, a=-7, b=-8

Step-by-step explanation:

x2+(a+b)x+36=0---(1)

x2+ax+12=0---(2)

x2+bx+15=0---(3)

solving 1 &2, we get

bx=-24---(4)

solving 1&3, we get

ax=-21---(5)

substitute 4&5 in (1)

we get x=3

then a=-7 &b=-8

Answer 2

Answer:

Value of a is -7 and b is -8

Step-by-step explanation:

Given equations are

${x}^{2} + (a + b)x + 36 = 0.........(i)$

${x}^{2} + ax + 12 = 0........(ii)$

${x}^{2} + bx + 15 = 0......(iii)$

Add equation (i) and (ii) and get

${x}^{2} + ax + 12 + {x}^{2} + bx + 15 = 0 \\ 2{x}^{2} + (a + b)x + 27 = 0......(iv)$

Equation (i) subtracted from equation (iv) and get,

${x}^{2} - 9= 0 \\ (x + 3)( x - 3) = 0 \\ x = 3 \: or \: - 3$

Putting value of x in equation (ii) and (iii), get

a=-7 and b= -8