Question

The zeroes of the polynomial 2x² - 9x + 10 are b) -8 a) 2, b) -2, c) -2,-5 d) 5,4​

Answer 1

Answer:

x = 5/2 or 2

Step-by-step explanation:

Given Quadratic equation → 2x² - 9x + 10

For finding the zeroes of any Quadratic equation, we first factorise it.

So, find out 2 numbers such that:

• Their product is 20 and
• Their sum is -9

The 2 numbers which satisfies these conditions are -5 and -4

On Splitting the middle term,

2x² - 9x + 10 = 0

⇒ 2x² - 4x - 5x + 10 = 0

⇒ 2x (x - 2) - 5 (x - 2) = 0

⇒ (2x - 5) (x - 2) = 0

This means that

• 2x - 5 = 0 ⇒  x = 5/2
• x - 2 = 0 ⇒  x = 2

Answer 2

$\Large\begin{gathered} {\underbrace{\boxed{ \rm {\green{Given}}}}}\end{gathered}$

$\Large{\textrm{{{\color{red}{2x² - 9x + 10 \: }}}}}$

_________________________

$\Large\begin{gathered} {\underbrace{\boxed{ \rm {\green{To \: \: Find}}}}}\end{gathered}$

We have to find the Zeros of polynomial.

_________________________

$\Large\begin{gathered} {\underbrace{\boxed{ \rm {\green{Solution}}}}}\end{gathered}$

Now , using the splitting the middle term method.

$\bf \large \rightarrow \: 2x² \: - \: 9x \: + \: 10 \: = \: 0$

$\bf \large \rightarrow \:2 {x}^{2} \: - 4x \: - 5x \: + 10 \: = \: 0$

$\bf \large \rightarrow \:2x \: \: (x - 2) \: \: - 5 \: \: (x - 2) \: = \: 0$

$\bf \large \rightarrow \:(2x - 5) \: \: \: (x - 2) \: \: = \: \: 0$

$\bf \large \rightarrow \:x \: = \frac{5}{2}$

$\bf \large \rightarrow \:x \: = \: 2$

⇨ Zeros of the polynomial is 5/2 and 2.