Question

Find the zeros of the quadratic polynomial(x2-5x+4)and verify the relation between the zeroes and the coefficients

Answer 1

Question :-

Find zeros of the quadratic -

→ x² - 5x + 4 = 0

Answer :-

→ zeros are 4 and 1

Solution :-

We have quadratic -

→ x² - 5x +4 = 0

Splitting the middle term

→ x² - 4x - x +4 = 0

→ x(x - 4) -1(x - 4) = 0

→ (x - 4)(x - 1) = 0

→ x = 4 or 1

Verification

If x = 4

→ (4)² - 5×4 + 4 = 0

→ 16 - 20+4 = 0

→ 20-20 = 0

If x = 1

→ (1)² - 5 + 4 = 0

→ 1 - 1 = 0

→ 0 = 0

Hence verified

Answer 2

To Find:
Zeroes of p(x) = x² - 5x + 4 = 0

Answer :-

zeros are 4 and 1

Solution :-

We have a quadratic polynomial,

x² - 5x +4 = 0

Splitting the middle term,

x² - 4x - x +4 = 0

x(x - 4) -1(x - 4) = 0

(x - 4)(x - 1) = 0

The factors of p(x) are (x-4) and (x-1)

That implies, x = 4    OR    1

Verification

α+β = -b/a
4+1= -(-5)/1
5=5

αβ = c/a
4*1 = 4/1
4=4

Hence, verified