+C =0 with rational coefficients is p + 19, then
13. If one root of the quadratic equation ax + bx + c = 0 with rational coefficient p+√q
other root is
Answers
The other root of given quadratic equation is (p - √q)
one root of the quadratic equation,ax² + bx + c = 0 with rational coefficient is p + √q.
as we know, p + √q is an irrational number.
so, other root must be an irrational number because we know sum and product of two conjugate irrational numbers is a rational number.
as (p + √q) + other root = -b/a = rational number
and (p + √q) other = c/a = rational number
so it is clear that the other root is conjugate of (p + √q) .i.e., (p - √q)
also read similar questions : prove that the roots of equations ax²+bx+c=0 and cx²+bx+a=0 are reciprocals of each other
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The other root is (p+√q) and (p-√q).
Given
To find the other root.
If one root of the quadratic equation ax² + bx + c = 0 with rational coefficient p + √q.
Quadratic equation is ax²+bx+c=0.
Where, a, b, c are rational numbers.
It has two roots α and β,
α+β = - b/a
αβ = c/a
They are rational numbers.
Here α = p+√q and β = p-√q. (By conjugate method)
Where, α = p+√q and β = p-√q are irrational numbers.
(α+β) = [(p+√q)+(p-√q)]
= [p+√q+p-√q]
= 2p
(α+β) = 2p
(αβ) = [(p+√q)(p-√q)]
= [p²-p√q+p√q-(√q×√q)]
= [p²-(√q)²]
= p²-q
αβ = p²-q
Therefore, the other root is (p+√q) and (p-√q).
To learn more...
1. brainly.in/question/1347322
2. brainly.in/question/11828765