Algebra> If the quadratic equations x 2 + ax + b =...

If the quadratic equations x2 + ax + b = 0 and x2 + bx + a = 0 (a ≠ b) have a common root, then the numerical value of a + b is . . . . . . . . . . . . . . .

Radhika Batra , 10 Years ago

Grade 11

2 Answers

Kevin Nash

Last Activity: 10 Years ago

According to the question, x2 + ax + b = 0 and x2 + bx + a = 0 (a ≠ b) have a common root, let it be α then we have

α 2 + 2 α + b = 0 . . . . . . . . . . . . (i)

α2 + b α + a = 0 . . . . . . . . . . . . (ii)

⇒ α2/a2 -b2 = α/b – a = 1/b – a ⇒ α2/a + b = α/-1 = 1/-1

⇒ α2 = - (a + b); α = 1 ⇒ a + b = -1

∴ Numerical value of a + b = -1

abhay

Last Activity: 7 Years ago

let the common root be z.

So, z²+az+b=0 and z²+bz+a=0 as per the given equations.

Equate them , z²+az+b=z²+bz+a

(a-b)z=a-b

so, z=1

put z in any of the 2 equations,

1² + b.1+a=0 or 1² +a.1+b=0

1+a+b=0 or 1+a+b=0

so from both the cases (a+b)=-1

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Algebra> If the quadratic equations x 2 + ax + b =...

If the quadratic equations x2 + ax + b = 0 and x2 + bx + a = 0 (a ≠ b) have a common root, then the numerical value of a + b is . . . . . . . . . . . . . . .

Radhika Batra , 10 Years ago

Kevin Nash

abhay

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