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fenix001 [56]
3 years ago
10

If the squared difference of the zeroes of the quadratic polynomial x2+kx+30 is equal to 169 find the value of k and the zeroes

Mathematics
1 answer:
anyanavicka [17]3 years ago
5 0

ANSWER

x  =  2 \: \: or \:  \:  x  =  15

Or

x  =   - 2 \: \: or \:  \:  x  =   -  15

EXPLANATION

The given polynomial is

f(x) = {x}^{2}  + kx + 30

where a=1,b=k, c=30

Let the zeroes of this polynomial be m and n.

Then the sum of roots is

m + n =  -  \frac{b}{a}  =  -k

and the product of roots is

mn =  \frac{c}{a}  = 30

The square difference of the zeroes is given by the expression.

( {m - n})^{2} =  {(m + n)}^{2} - 4mn

From the question, this difference is 169.

This implies that:

( { - k)}^{2}  - 4(30) = 169

{  k}^{2}  -120= 169

k^{2} = 289

k=  \pm \sqrt{289}

k=  \pm17

We substitute the values of k into the equation and solve for x.

f(x) = {x}^{2}   \pm17x + 30

f(x) = (x  \pm2)(x  \pm 15)

The zeroes are given by;

(x  \pm2)(x  \pm 15) = 0

x  =  \pm2 \: \: or \:  \:  x  =  \pm 15

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