Question

find the zeroes of 2X square+4-9xand verify the relationship between zeroes and coefficient​

Answer 1

Step-by-step explanation:

Given -

• p(x) = 2x² - 9x + 4

To Find -

• Zeroes of the polynomial and verify the relationship between the zeroes and the coefficient.

Now,

→ 2x² - 9x + 4

By using quadratic formula :-

• x = -b ± √b² - 4ac/2a

→ -(-9) ± √(9)² - 4×(2)×(4)/2(2)

→ 9 ± √81 - 32/4

→ 9 ± √49/4

→ 9 ± 7/4

Zeroes are -

→ x = 9 + 7/4

→ 16/4

→ 4

And

→ x = 9 - 7/4

→ 2/4

→ 1/2

Hence,

The zeroes are 4 and 1/2

Verification :-

• α + β = -b/a

→ 4 + 1/2 = -(-9)/2

→ 8+1/2 = 9/2

→ 9/2 = 9/2

LHS = RHS

And

• αβ = c/a

→ 4 × 1/2 = 4/2

→ 2 = 2

LHS = RHS

Hence,

Verified...

It shows that our answer is absolutely correct.

Answer 2

Given:-

• P(x) :- 2x² - 9x + 4

To find :-

• Zeroes of polynomial and verify relationship b/w zeroes and coefficient

Solution:-

★ Using quadratic formula:-

$\implies \large\bold{\underline{\boxed{\sf{\purple{\dag \; x = -b ± \dfrac{\sqrt{ b^2 - 4ac}}{2a}}}}}}$

$\implies \sf{ -(-9) ± \dfrac{\sqrt{(9)^2 - 4 × 2 × 4}}{2×2}}$

$\implies \sf{ (9) ± \dfrac{\sqrt{( 81 - 32}}{4}}$

$\implies \sf{ (9) ± \dfrac{\sqrt{( 49 }}{4}}$

$\implies \sf{ (9) ± \dfrac{\sqrt{(7}}{4}}$

$\bullet \sf{ Either \; x = 9 + \dfrac{7}{4} \; or \; x = 9 - \dfrac{7}{4}}$

So, zeroes are:-

$\implies \sf{ 9 + \dfrac{7}{4}}$

$\implies \sf{ \dfrac{16}{4}}$

$\implies \sf{4}$

And,

$\implies \sf{ \dfrac{2}{4}}$

$\implies \sf{ \dfrac{16}{4}}$

$\implies \sf{ \dfrac{1}{2}}$

So,

Zeroes of the given polynomial are 4 and 1/2

★ Verifying relationship b/w zeroes and coefficient:-

$\bullet \sf{ Sum \; of \; zeroes:-}$

• $\sf{ \alpha + \beta = \dfrac{-b}{a}}$

• $\sf{ 4 + \dfrac{1}{2} = - \bigg( \dfrac{-9}{2} \bigg)}$

• $\sf{ \dfrac{ 8 + 1}{2} = \bigg( \dfrac{9}{2} \bigg)}$

• $\sf{ \dfrac{9}{2} = \bigg( \dfrac{9}{2} \bigg)}$

• LHS = RHS

$\bullet \sf{ Product \; of \; zeroes:-}$

• $\sf{ \alpha \beta = \dfrac{c}{a}}$

• $\sf{ 4 × \dfrac{1}{2} = \dfrac{4}{2}}$

• $\sf{ 2 = 2}$

• LHS = RHS

$\bold{\underline{\underline{\sf{\purple{Hence, \; Verified}}}}}$

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