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Grade 9Algebra

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 . . . . . . . . . . . . . . .

Profile image of Thrinath
8 Years agoGrade 9
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1 Answer

Profile image of Surya
8 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

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