If 1 root of the qua dratic equation 3x²-px-2=0 is 2,then find the value of p also find the other root
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One root of the quadratic equation 3x²-px-2=0 -----------(1) is 2.
Let the other root is α.
Then from the relation between the roots and the coefficients of a quadratic equation we have,
α+2=-(-p/3)
or, α+2=p/3 ---------(2)
α×2=-2/3 ------------(3)
or, α=-2/3×1/2
or, α=-1/3
Putting in (2) we get,
-1/3+2=p/3
or, p/3=(6-1)/3
or, p/3=5/3
or, p=5
∴, p=5 and the other root is -1/3. (Answer)
Let the other root is α.
Then from the relation between the roots and the coefficients of a quadratic equation we have,
α+2=-(-p/3)
or, α+2=p/3 ---------(2)
α×2=-2/3 ------------(3)
or, α=-2/3×1/2
or, α=-1/3
Putting in (2) we get,
-1/3+2=p/3
or, p/3=(6-1)/3
or, p/3=5/3
or, p=5
∴, p=5 and the other root is -1/3. (Answer)
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