If the equations x² + ax + 12 = 0, x² + bx + 15 = 0 and x² + (a + b)x + 36 = 0 have a common positive root, then ab equals to ________.
Answers
Answer:
answer 3
x2 +ax +12=0,_(1)
x2+bx+15=0,_(2)
x2+(a+b )x+36=0_(3)
let the common root be m
so,m will setisty all three equation
m2
ading 5and 6
2am का स्क्वायर प्लस ए ब्रैकेट ए प्लस बी एम प्लस 7 इक्वल टू जीरो subtraining 6from7
एम का स्क्वायर माइनस 9 स्क्वायर एमएम 1 लाइन और इक्वल - 3 पैकेट व्हिच इज नॉट पॉसिबल
Solution!!
x² + ax + 12 = 0...(1)
x² + bx + 15 = 0...(2)
x² + (a + b)x + 36 = 0...(3)
Adding (1) and (2), we get,
2x² + (a + b)x + 27 = 0...(4)
Subtracting (3) and (4), we get,
-x² + 9 = 0
x² = 9
x = √9
x = 3
Putting the value of 'x' in (1),
x² + ax + 12 = 0
3² + 3a + 12 = 0
9 + 3a + 12 = 0
3a + 21 = 0
3a = -21
a = -7
Putting the value of 'x' in (2),
x² + bx + 15 = 0
3² + 3b + 15 = 0
9 + 3b + 15 = 0
3b + 24 = 0
3b = -24
b = -8
ab = -7 × (-8)
ab = 56
If the equations x² + ax + 12 = 0, x² + bx + 15 = 0 and x² + (a + b)x + 36 = 0 have a common positive root, then ab equals to 56.