Question

find the zeroes of quadratic polynomial x²-5x and verify the relationship between the zeroes and the coefficients.​

Answer 1

Correct Question:

Find the zeroes of quadratic polynomial (x² - 5x + 6) and verify the relationship between the zeroes and the coefficients.

$\huge\mathfrak{Answer:}$

Given:

• We have been given a quadratic polynomial (x² - 5x + 6).

To Find:

• We need to find the zeroes of this polynomial and also verify the relationship between the zeroes and coefficients of this polynomial.

Solution:

The given polynomial is (x² - 5x + 6).

We can find the zeroes of this polynomial by the method of splitting the middle term.

We need to find two such numbers whose sum is -5 and product is 6.

Two such numbers are -3 and -2.

Substituting the values, we have

x² - 3x - 2x + 6 = 0

=> x(x - 3) -2(x - 3)

=> (x - 3) (x - 2)

Either (x - 3)= 0 or (x - 2) = 0.

When (x - 3) = 0

=> x = 3

When (x - 2) = 0

=> x = 2

Therefore, zeroes of this polynomial are 3 and 2.

α = 3 and β = 2

Now, we need to verify the relationship between zeroes and coefficients, we have

Sum of zeroes (α + β)

= 3 + 2

= 5 = (-b/a)

Product of zeroes (αβ)

= 3 × 2

= 6 = (c/a)

Hence, relationship between zeroes and coefficients is verified!!

Answer 2

★ qUESTIOn ★

find the zeroes of quadratic polynomial x²-5x and verify the relationship between the zeroes and the coefficients.

$\rule{300}2$

★ aNSWEr ★

Mate your question is incomplete please check your question

but similar question is solved here check it.

★ CorrecT qUESTIOn ★

find the zeroes of quadratic polynomial 【x²-5x+4】 and verify the relationship between the zeroes and the coefficients.

• BY SPLITTING METHOD→

$\implies x^2-5x+4=0\\ \implies x^2-4x-x+4=0\\ \implies x(x-4)-1(x-4)=0\\ \implies (x-1)(x-4)=0\\ \implies x=1,x=4$

So the zeroes are = 1 and 4

◇ Verification ◇

→ x=1

→ Then,

$\implies x2-5x+4=0\\ \implies (1)^2-5(1)+4=0\\ \implies 1-5+4=0 \\ \implies 5-5=0\\ \implies 0=0$

Verified√√

→ ∆gain,

→ if x=4

Then,

$\implies x^2-5x+4=0\\ \implies 4^2-5(4)+4=0\\ \implies 16-20+4=0\\ \implies 20-20=0\\ \implies 0=0$

Verified √√

$\rule{150}2$

Hence,

→ the relationship between the zeroes and the coefficients is... 【√erified】