A quadratic Equation with roots 7+i and 7-i is.... ?

Question

That's the questions and the choices are.. :
1) x^2-14+50=0
2)X^2+14x+50=0
3)X^2-14x+48=0
4)X^2+14x+48=0

Answer 1

To find the equation, just substitute the 2 roots to the "Quadramagic formula" (...)
x² - (p + q)x + pq = 0
where p and q are the roots.

Hence, p = 7 + i and q = 7 - i. We substitute:
x² - [(7 + i) + (7 - i)]x + (7 + i)(7 - i) = 0

We add and multiply
x² - (14)x + (7² - i²) = 0

Since i² = -1, then
x² - 14x + 49 - (-1) = 0

then,
x² - 14x + 49 + 1 = 0

Therefore, the quadratic equation is
x² - 14x + 50 = 0

Therefore, the correct answer is 1).

^_^

Answer 2

X^2+14x+50=0

Answer 3

2

Answer 4

the equation

(x-7)^2 - i^2 = 0

or x^2-14x+ 50 = 0

Answer 5

turn roots into aspects x = 7 ==> (x - 7) = 0 and (x - 7) is a element x = -2/3 ==> (x + 2/3) = 0, and (x + 2/3) is a element multiply the 2d element via 3 ==> (3x + 2) = 0 is the extra accepted element with x = -2/3 as a root (x - 7)(3x + 2) = 0 3x^2 - 19x - 14 = 0 is one such quadratic you additionally can multiply this via any actual variety to maintain an analogous roots

Answer 6

Using quad. formula on (1)

x = ( -b +- sqrt(b^2 - 4ac) ) / 2a, a=1, b=-14, c=50
x = ( -(-14) +- sqrt( (-14)^2 - 4(1)(50) ) ) / 2(1)
x = ( 14 +- sqrt(196 - 200) ) / 2
x = ( 14 +- sqrt(-4) ) / 2
x = ( 14 +- 2*sqrt(-1) ) / 2
x = 7 +- sqrt(-1)
x = 7+i, 7-i

try the quad. form on 2-4 to confirm that...

roots of (2) are -7+i & -7-i
root of (3) is +7
root of (4) is -7


Or get the answer directly by foiling

[x - (7- i)][x - (7 + i)]
x^2 - x(7- i) - x(7+i) + (7-i)(7+i)
x^2 - 7x + ix -7x -ix + 49 + 7i -7i -i^2
x^2 - 14x + 49 + i^2
x^2 - 14x + 49 - (-1)
x^2 - 14x + 50

Answer 7

answer

=x^2-x(sum 0f the roots)+(product of the roots)
=x^2-x(7+i+7-i)+(7+i)(7-i)
=x^2-x(14)+(49+1)
=x^2-14x+50

this is the right answer and it's not given in the choise list

Answer 8

No. 2 is the correct answer.

Given 7+ ì and 7- ì as roots.
→ x = 7+ ì (or) x = 7- ì
(x - 7- ì )(x - 7 + ì) = 0 [multiply out].
x² -7x + x ì - 7x + 49 - 7 ì - x ì + 7 ì - ì² = 0
x² -14x + 49 - ì² = 0
x² -14x + 49 - (√-1)² = 0
x² -14x + 49 + 1 = 0
x² -14x + 50 = 0

Answer 9

Let a*x^2+b*x+c=0 be quadratic with roots m=7+i,n=7-i

=>-b/a=m+n=14 (Sum of the roots)

=>b/a=-14.....................................1


Also,
c/a=m*n=(7+i)(7-i)=49-(-1)=50 (Product of roots)

c/a=50........................2

As in all cases a=1,we have

c=50
b=-14

AND HENCE THE CORRECT OPTION IS ((((1))))

Answer 10

I think none of these is the right answer because when you get the products of the roots one part of the answer is 49 which is not given in any part of the choices.