Question

find zeros of quadratic polynomial 4 x square - 4 x minus 3 and verify the relationship between zeros and coefficient​

Answer 1

Answer:

answer is x= -1/2 or x= 3/2

Step-by-step explanation:

please refer the above image in which i have solved the question ..Thankyou

Answer 2

✯✯ QUESTION ✯✯

Find Zeroes of Quadratic Polynomial 4x²-4x-3 and verify the relationship between zeroes and cofficients..

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✰✰ ANSWER ✰✰

$\longmapsto\tt{{4x}^{2}-4x-3}$

➥Splitting Middle Term : -

$\longmapsto\tt{{4x}^{2}-(6x-2x)-3}$

$\longmapsto\tt{{4x}^{2}-6x+2x-3}$

$\longmapsto\tt{2x(2x-3)+1(2x-3)}$

$\longmapsto\tt{(2x+1)(2x-3)}$

$\checkmark\tt{2x+1=0}$

$\longmapsto\tt{x=\dfrac{-1}{2}}$

$\checkmark\tt{2x-3=0}$

$\longmapsto\tt{x=\dfrac{3}{2}}$

➙So, -1/2 and 3/2 are the zeroes of the polynomial 4x²-4x-3..

★Sum of Zeroes : -

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

$\longmapsto\tt{\dfrac{-1}{2}+\dfrac{3}{2}=\dfrac{-(-4)}{4}}$

$\longmapsto\tt{\dfrac{-1+3}{2}=\dfrac{4}{4}}$

$\longmapsto\tt{\cancel\dfrac{2}{2}=\dfrac{4}{4}}$

$\longmapsto\tt{0=0}$

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

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★Product of Zeroes : -

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

$\longmapsto\tt{\dfrac{-1}{2}\times\dfrac{3}{2}=\dfrac{-3}{4}}$

$\longmapsto\tt{\dfrac{-3}{4}=\dfrac{-3}{4}}$

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

✺ HENCE VERIFIED ✺