Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficient.

${4u}^{2}+8u$


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Answer 1

Answer:

⋆ Given Polynomial : 4u² + 8u

Here : a = 4,⠀b = 8,⠀c = 0

$:\implies\tt f(x) = 0\\\\\\:\implies\tt 4u^2 +8u= 0\\\\\\:\implies\tt 4u(u+2)= 0\\\\\\:\implies\underline{\boxed{\tt u =0\quad or\quad u=-\:2}}$

$\rule{150}{1}$

$\underline{\bigstar\:\textsf{Relation b/w zeroes and coefficient :}}$

$\qquad\underline{\bf{\dag}\:\:\textsf{Sum of Zeroes :}}\\\dashrightarrow\tt\:\: \alpha+\beta = \dfrac{-\:b}{a}\\\\\\\dashrightarrow\tt\:\: 0 + (-\:2) = \dfrac{-8}{4}\\\\\\\dashrightarrow\:\:\underline{\boxed{\red{\tt -\:2=-\:2}}}\\\\\\{\qquad\underline{\bf{\dag}\:\:\textsf{Product of Zeroes :}}}\\\\\dashrightarrow\tt\:\: \alpha \times \beta = \dfrac{c}{a}\\\\\\\dashrightarrow\tt\:\: 0\times (-\:2) = \dfrac{0}{4}\\\\\\\dashrightarrow\:\:\underline{\boxed{ \red{\tt 0=0}}}$

Answer 2

Step-by-step explanation:

Given -

p(u) = 4u² + 8u

To Find -

• Zeroes of the polynomial
• Verify the relation between the zeroes and the coefficient

Now,

» 4u² + 8u = 0

» 4u(u + 2) = 0

Then,

Zeroes are -

4u = 0 and u + 2 = 0

• u = 0 and u = -2

Verification -

As we know that :-

• α + β = -b/a

» 0 + (-2) = -(8)/4

» -2 = -2

LHS = RHS

And

• αβ = c/a

» 0 × -2 = 0/4

» 0 = 0

LHS = RHS

Hence,

Verified..