Question

Find the sum of the zeros of a polynomial
x2–x–4.​

Answer 1

Answer:

1

Step-by-step explanation:

Quadratic equation is given by x^2 - (sum of zeros) x + (product of zeros)

Answer 2

$\huge\bold{Question:-}$

Find the sum of the zeroes of a polynomial

${x}^{2} - x - 4$

$\huge\bold{Solution:-}$

Factorise

${x}^{2} - x - 4$

We have,

Zeroes of Quadratic equation is

=>$\frac{ - b ± \sqrt{ {b}^{2} - 4ac} }{2a}$

So,

=>$x = \frac{ - ( - 1) ± \sqrt{ {( - 1)}^{2} - 4(1)( - 4) } }{2(1)}$

=>$\frac{1 ± \sqrt{1 + 16} }{2}$

=>$\frac{1 ± \sqrt{17} }{2}$

=>$\frac{1 + \sqrt{17} }{2}$

And

=>$\frac{1 - \sqrt{17} }{2}$

Sum of zeroes is

=$\frac{1 + \sqrt{17} }{2} + \frac{1 - \sqrt{17} }{2}$

$\frac{1 + \sqrt{17} + 1 - \sqrt{17} }{2}$

=>$\frac{2}{2} = 1$

$\huge\bold{Final Answer:-}$

Sum of zeroes of x²-x- 4 = 1