Question

II.
Factorise the fol
2
(1) 24a’ + 37a - 5​

Answer 1

Step-by-step explanation:

Correct question :-

• Factorise the given polynomial p(a) = 24a² + 37a - 5

To Find -

• Zeroes of the polynomial

Solution :-

Now,

→ 24a² + 37a - 5

By middle term splitt :-

→ 24a² + 40a - 3a - 5

→ 8a(3a + 5) - 1(3a + 5)

→ (8a - 1)(3a + 5)

Zeroes are -

→ 8a - 1 = 0 and 3a + 5 = 0

→ a = 1/8 and a = -5/3

Verification :-

• α + β = -b/a

→ -5/3 + 1/8 = -(37)/24

→ -40 + 3/24 = -37/24

→ -37/24 = -37/24

LHS = RHS

And

• αβ = c/a

→ -5/3 × 1/8 = -5/24

→ -5/24 = -5/24

LHS = RHS

Hence,

Verified...

It shows that our answer is absolutely correct.

Answer 2

Given:-

• 24a² + 37a -5

To find:-

• Zeroes of polynomial

Solution:-

$\sf\boxed{ 24a^2 + 37a - 5 = 0}$

24a² + 40a - 3a -5 = 0

8a(3a + 5) -1(3a + 5) = 0

(8a - 1)(3a + 5) = 0

Both (8a - 1) and (3a + 5) is equal to 0.

8a - 1 = 0 and 3a + 5 = 0

a = $\sf{ \dfrac{1}{8}}$ and a = $\sf{ \dfrac{-5}{3}}$

★ Verification:-

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

$\implies \sf{ \dfrac{1}{8} - \dfrac{-5}{3} = \dfrac{-37}{24}}$

$\implies \sf{ \dfrac{ 3 - 40}{24} = \dfrac{ -37}{24}}$

$\implies \sf{ \dfrac{-37}{24} = \dfrac{-37}{24}}$

LHS = RHS

$\implies \sf{ \alpha \beta = \dfrac{c}{a}}$

$\implies \sf{ \dfrac{-5}{3} \times \dfrac{1}{8} = \dfrac{-5}{24}}$

$\implies \sf{ \dfrac{-5}{24} = \dfrac{-5}{24}}$

LHS = RHS

★ Hence, Verified!

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