Quadratic Formula Equation?

if you know the formula it is easy

(-b + or - sqrt(b^2 - 4ac))/2a

so for t^2 + 13t + 42 = 0

a = 1

b = 13

c = 42

and you just plug those in

(-(13) + or - sqrt(13^2 - 4(1)(42))/2(1)

(-13 + or - sqrt(169 - 168) / 2

(-13 + or - sqrt(1)) /2

(-13 + or - 1) /2

t = (-13 + 1)/2 and t = (-13 -1)/2

t = (-12)/2 and t = (-14)/2

t = -6 and t = -7

without doing the quadratic forumula you could have just tried to factor it.

what two numbers multiply to 42 and add up to 13? 6 and 7

(t+6)(t+7) = 0

t + 6 = 0; t = -6

t + 7 = 0; t = -7

Quadratic formula is:

[-b +/- sqrt(b^2 - 4ac)] / 2a

Your equation: t2 + 13t + 42 = 0

a = 1, b = 13, c = 42

[-13 +/- sqrt(13^2 - 4 * 1 * 42)] / (2 * 1)

[-13 +/- sqrt(169 - 168)] / 2

[-13 +/- sqrt(1)] / 2

[-13 +/- 1] / 2

(-13 + 1) / 2 or (-13 - 1) / 2

-12 / 2 or -14 / 2

-6 or -7

Delta = 13^2 - 4*42 = 169 - 168 = 1 = 1^2

From there, the two roots are:

t1 = (-13 - sqrt(Delta))/2 = (-14)/2 = -7

t2 = (-13 + sqrt(Delta))/2 = -12/2 = -6

t² + 13t + 42 = 0

Forumla is:

t = (-b ± √(b² - 4ac))/2a

t = (-13 ± √(13² - 4(1)(42)))/2(1)

t = (-13 ± √(169 - 168))/2

t = (-13 ± √1)/2

t = (-13 ± 1)/2

t = (-13 + 1)/2 and (-13 - 1)/2

t = (-12)/2 and (-14)/2

t = -6 and -7

I think the formula is t^2 + 13t + 42

so,

(-b +- sqrt(b^2 - 4ac)) / 2a

is

(-13 +- sqrt(169 - 168)) / 2

is

(-13 +- 1) / 2

is

-14/2 = -7

or

-12/2 = -6

t^2 + 13t + 42 = 0

first calculate the delta:

delta = b^2 - 4ac = 169 - 4*1*42 = 169 - 168 = 1

root(delta) = 1

then the roots are: x = (-b-root(delta))/2 or (-b+root(delta))/2

therefore

x= (-13-1)/2 or x= (-13+1)/2

x=-7 or x=-6

good luck to you in your future solutions! ;)

t = [-13 +/- sqrt(13^2 -4(1)(42))]/(2*1)

t = [-13 +/- sqrt(169 -168)]/2

t = [-13 +/- 1]/2

t = (-13 + 1)/2 = -6

t = (-13 - 1)/2 = -7

aha

T^2 + 13T + 42 = 0

first - get the factors for 42

(1,42) (2,21) (3,14)(6,7)

NOW - which set of factors, when added together, have a sum of 13 (since both 2nd and third parts are +)

(t + ___) ( t + ____)

u can fill in the blanks - all the best

A = 1

B = 13

C = 42

Just plug it into the formula