so far i have solved the answer to part a).

but i can't seem to solve the equation for part b) though. to solve this qudractic do i have to use the qaudractic formula?

any help is appreichated thank you.

:D

Printable View

- December 3rd 2005, 12:31 PMrpatelsolving this equation problem
so far i have solved the answer to part a).

but i can't seem to solve the equation for part b) though. to solve this qudractic do i have to use the qaudractic formula?

any help is appreichated thank you.

:D - December 3rd 2005, 02:57 PMRich B.Hi Rpatel:

Strictly speaking, the quadratic formula is nor required in this instance because the trinomial 10x^2-11x-84 is factorable. FYI, any quadratic trinomial, ax^2+bx+c, is factorable whenever its discriminant, b^2-4ac, is a perfect square. In the present case, b^2-4ac = (-11)^2 - 4(10)(-84) = 3481, which is indeed a perfect square (Any integer, k, is a*perfect square*if sqrt(k) is itself an integer. Because sqrt(3481)=59, and 59 is an integer, it follows that 3481 is by definition a perfect square). Nevertheless, were this*my*problem, I would use the q.formula just the same, as the coefficients 10 and 84 make for more factor combinations than I care to test.

Regards,

Rich B. - December 3rd 2005, 04:14 PMticbolQuote:

Originally Posted by**rpatel**

Your 10x^2 -11x -84 = 0 is correct per shown figure.

And that gives x = 3.5cm or -2.4cm

x=3.5 fails at x-7.

3.5 -7 = -3.5cm ------cannot be. No negative dimensions.

x = -2.4m ------cannot be. - December 3rd 2005, 10:40 PMCaptainBlackQuote:

Originally Posted by**Rich B.**

In what sense? By the Fundamental Theorem of Algebra every

quadratic has a root, and so is factorisable. It's just that these

roots may not be real, or rational.

Quote:

FYI, any quadratic trinomial, ax^2+bx+c, is factorable whenever its discriminant, b^2-4ac, is a perfect square.

For instance the discriminant of: is 8, which

is not a perfect square, but that does not mean we cannot factorise it:

.

When the discriminant is a perfect square it does ensure that

the roots are rational.

Quote:

In the present case, b^2-4ac = (-11)^2 - 4(10)(-84) = 3481, which is indeed a perfect square (Any integer, k, is a*perfect square*if sqrt(k) is itself an integer. Because sqrt(3481)=59, and 59 is an integer, it follows that 3481 is by definition a perfect square). Nevertheless, were this*my*problem, I would use the q.formula just the same, as the coefficients 10 and 84 make for more factor combinations than I care to test.

Quote:

Regards,

Rich B.

is a perfect square you have done almost all the work involved

in finding the roots using the quadratic formula and may as well

go ahead and find them that way, and then complete the factorisation,

or not (in this case we are interested in the roots not the factors).

RonL