Question

find the zeros of the quadratic polynomial 8x square + 2 x minus 15 and verify the relationship between the zeros and its coefficient

Answer 1

Solution :

Factororise : 8x² + 2x - 15

= 8x² - 10x + 12x - 15

= 2x ( 4x - 5 ) + 3 ( 4x - 5 )

= ( 2x + 3 ) ( 4x - 5 )

TO FIND THE ZEROES :

2x + 3 = 0

=> 2x = - 3

=> x = -3/2

∴ α = - 3/2

Also,

4x - 5 = 0

=> 4x = 5

=> x = 5/4

∴ β = 5/4

Now,

VERIFICATION :

Here, a = 8 ; b = 2 and c = - 15

→ α + β = - b/a

=> -3/2 + 5/4 = - 2/8

=> -6 + 5/4 = -1/4

=> -1/4 = -1/4

∴ L.H.S = R.H.S

Also,

→ αβ = c/a

=> -3/2 × 5/4 = -15/8

=> -15/8 = -15/8

∴ L.H.S = R.H.S

Hence proved!

$\rule{200}2$

Answer 2

✯✯ QUESTION ✯✯

find the zeros of the quadratic polynomial 8x²+ 2x- 15 and verify the relationship between the zeros and its coefficient..

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✰✰ ANSWER ✰✰

$\longmapsto\tt{{8x}^{2}+2x-15}$

By Splitting Middle Term : -

$\longmapsto\tt{{8}^{2}+2x-15=0}$

$\longmapsto\tt{{8x}^{2}+12x-10x-15=0}$

$\longmapsto\tt{4x(2x+3)-5(2x+3)}$

$\longmapsto\tt{(4x-5)(2x+3)}$

• x = 5/4
• x = -3/2

➮So , 5/4 and -3/2 are the zeroes of polynomial 8x²+2x-15..

➥Here : -

• a = 8
• b = 2
• c = -15

★Sum of Zeroes : -

$\longmapsto\tt{\alpha+\beta=\dfrac{-b}{a}}$

$\longmapsto\tt{\dfrac{5}{4}+\dfrac{-3}{2}=\dfrac{(-2)}{8}}$

$\longmapsto\tt{\dfrac{5-6}{4}=\cancel\dfrac{-2}{8}}$

$\longmapsto\tt\bold{\dfrac{-1}{4}=\dfrac{-1}{4}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{L.H.S}\orange{=}\purple{R.H.S}}}$

★Product Of Zeroes : -

$\longmapsto\tt\bold{\alpha\beta=\dfrac{c}{a}}$

$\longmapsto\tt{\dfrac{5}{4}\times{\dfrac{-3}{2}}=\dfrac{-15}{8}}$

$\longmapsto\tt\bold{\dfrac{-15}{8}=\dfrac{-15}{8}}$

$\pink\longmapsto\:\large\underline{\boxed{\bf\purple{L.H.S}\red{=}\green{R.H.S}}}$

✺ HENCE VERIFIED ✺