The sum of the squares of the roots of the equation x^2+2hx=3 is 10. The absolute value of h is equal to:

1971 AMC 12 Problem 20

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20.

The sum of the squares of the roots of the equation

x^2+2hx=3

10.

The absolute value of

h

is equal to:

-1

\frac{1}{2}

\frac{2}{3}

2

None of these

Use the sum and product of the two roots

If the roots are

r,s,

then

r+s=-2h

and

rs=-3

For roots

r,s,

Vieta’s formulas give

r+s=-2h

and

rs=-3.

Hence

\begin{aligned} 4h^2=(r+s)^2 &=r^2+s^2+2rs\\ &=10-6=4. \end{aligned}

Therefore

|h|=1,

which is not among choices A-D because choice A is

-1.

Therefore, the correct answer is E.