x² + Ca-l)x+ b
are 2 and - 3
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Answer:
We know that if m and n are the roots of a quadratic equation ax
2
+bx+c=0, then the sum of the roots is (m+n) and the product of the roots is (mn). And then the quadratic equation becomes x
2
−(m+n)x+mn=0
Here, it is given that the roots of the quadratic equation are m=(2+
3
) and n=(2−
3
), therefore,
The sum of the roots is:
m+n=2+
3
+2−
3
=2+2=4
And the product of the roots is:
mn=(2+
3
)×(2−
3
)=2
2
−(
3
)
2
=4−3=1(∵a
2
−b
2
=(a−b)(a+b))
Therefore, the required quadratic equation is
x
2
−(m+n)x+mn=0
⇒x
2
−4x+1=0
Hence, x
2
−4x+1=0 is the quadratic equation whose roots are (2+
3
) and (2−
3
).
Explanation:
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