Quadratic Equation: Condition for Roots Given, Coefficient Must be Figured Out

**quadrat** · November 29th 2010, 05:33 AM

The question is:

If one of the roots of x2 + ax + 4 = 0 is twice the other root, then the value of 'a' is?

(A) -3(2)0.5
(B) 8(2)0.5
(C) (2)0.5
(D) -2(2)0.5

I have no idea what to do...please help.

**emakarov** · November 29th 2010, 06:22 AM

If a quadratic equation $x^2+ax+b=0$ has roots $x_1,x_2$ , then $x^2+ax+b=(x-x_1)(x-x_2)$ . Also, two polynomials are equal iff their respective coefficients are equal.

According to my calculations, the answer is "none of the above" because one variant is only a partial, not complete, answer.

In typing polynomials in ASCII, it is customary to indicate power using ^, e.g.: x^2 + ax + 4. You can also use LaTeX: type [tex]x^2+ax+4[/tex] and [tex]\sqrt{2}[/tex] to get $x^2+ax+4$ and $\sqrt{2}$ .

**earboth** · November 29th 2010, 06:36 AM

Originally Posted by quadrat

The question is:

If one of the roots of x2 + ax + 4 = 0 is twice the other root, then the value of 'a' is?

(A) -3(2)0.5
(B) 8(2)0.5
(C) (2)0.5
(D) -2(2)0.5

I have no idea what to do...please help.

1. Solve the equation

$x^2+ax+4=0$ for x.

You should come out with:

$x_1 = -\frac a2-\sqrt{\frac{a^2}4-4}~\vee~x_1 = -\frac a2+\sqrt{\frac{a^2}4-4}$

2. According to the text of the peoblem you know that

$2x_1 = x_2$ . That means:

$2\cdot \left(-\frac a2-\sqrt{\frac{a^2}4-4}\right)= -\frac a2+\sqrt{\frac{a^2}4-4}$

Solve for a.

3. Btw I've got 2 different values for a. But please check my calculations!

**HallsofIvy** · November 29th 2010, 11:26 AM

Yet another variation: Let $x_1$ be one of the roots- the other is $2x_1$ . Then we have $(x- x_1)(x- 2x_1)= x^2- (x_1+ 2x_1)+ 2x_1^2= x^2- 3x_1x+ 2x_1^2= x^2+ ax+ 4$
Now you know that $2x_1^2= 4$ and $a= -3x_1$ . Yes, there are two possible values for a but only one of them is one of the choices.

**mr fantastic** · November 29th 2010, 05:05 PM

Originally Posted by quadrat

The question is:

If one of the roots of x2 + ax + 4 = 0 is twice the other root, then the value of 'a' is?

(A) -3(2)0.5
(B) 8(2)0.5
(C) (2)0.5
(D) -2(2)0.5

I have no idea what to do...please help.

If you can't write $x^2$ , then please at least use x^2 so that what you post is more easily read etc.

Thread: Quadratic Equation: Condition for Roots Given, Coefficient Must be Figured Out

LinkBack

Thread Tools

Display

Quadratic Equation: Condition for Roots Given, Coefficient Must be Figured Out

Similar Math Help Forum Discussions

Probability with random-coefficient quadratic equation

Roots of a quadratic equation .

Roots of Quadratic Equation

Roots of a quadratic equation

Quadratic equation from given roots.

Search Tags