Question 603470: Hi,
Can someone help me please?
write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form ax^2+bx+c=0.
-√̅10, 6√̅10
Thanks,
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
You are either expecting a quadratic with irrational coefficients or you have a typo in your rendering. You have some sort of symbol, other than the radical, in your rendering of the two solutions. Ignoring that because I have no other choice, I'm assuming that your two solution numbers are:
and
Irrational roots of quadratics with rational cooefficients ALWAYS come in conjugate pairs, but quadratics always have exactly 2 roots, therefore with the two given roots the first degree term will have an irrational coefficient:
If  is a root (or solution, if you prefer) of a polynomial equation, then  is a factor of the polynomial. Hence, for your two given numbers, the two factors of the quadratic are:
and
the product of which is:
Hence the desired equation is:
John
My calculator said it, I believe it, that settles it
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