Question

Two quadratic equation x2 - bx + 6 = 0 and x2 - 6x + c = 0 have a common root. if the remaining roots of the first and second equation are positive integers and are in the ratio 3 : 4 respectively , then the common root is

Answer 1

Step-by-step explanation:

α2−bα+6=0

α2−6α+c=0

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(6−b)α+6−c=0

α=6−bc−6

α.3a=6⇒a=α2

α+4a=6

α+α4×2=6

α2+8−6α=0

α2−6α+8=0

(α−4)(α−2)=0

α=4,2

Answer 2

Answer:

$(a - 2)(b - 4) = 0 \\ a = 2 \: b = 4$