2.3 Relationship: Zeroes & Coefficients

Step 1

Factorize the polynomial by splitting the middle term: $x^2 + 2x + 5x + 10$ .

Step 2

$x(x+2) + 5(x+2) = (x+2)(x+5)$ .

Step 3

Zeroes are $x = -2$ and $x = -5$ . So $\alpha = -2, \beta = -5$ .

Step 4

Verification: Sum = $(-2) + (-5) = -7$ . From formula: $-b/a = -7/1 = -7$ . Matched.

Step 5

Product = $(-2)(-5) = 10$ . From formula: $c/a = 10/1 = 10$ . Matched.

Final Answer

Zeroes: -2, -5. Verified.

Operation

Polynomial: ax^3 + bx^2 + cx + d

a (x^3 coeff)

b (x^2 coeff)

c (x coeff)

d (constant)

x value

y value

z value

Select an operation and enter values.