Question

find the value of a and b where ax square +bx + c =0 and x=1 , x=2 ​

Answer 1

Given:-

• Quadratic polynomial is ax² + bc + c in which x = 1 and x = 2

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To find:-

• Value of a and b

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$\huge \tt \: ☃\:Solution$

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Roots or we can say Zero's of polynomial are 1 and 2.

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Sum of Zero's = α + β = $\frac{coefficient\:of\:x}{coefficient\:of\:x² }$

So,

Sum of Zero's = 1 + 2 = $\frac{3}{ 1}=\frac{coefficient\:of\:x}{coefficient\:of\:x² }$

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Product of Zero's = αβ = $\frac{Constant\:term}{coefficient\:of\:x² }$

So,

Sum of Zero's = 1 × 2 = $\frac{2}{ 1}=\frac{constant\:term}{coefficient\:of\:x² }$

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Therefore,

Sum of zero's = 3

Product of zero's = 2

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We know that,

If we have sum of zero's and product of zero's, then the equation will be

⍈ x² - ( sum of zero's)x + (product of zero's)

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Put values,

⇢x² - (3)x + 2

⇢x² - 3x + 2

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Verification:-

⇢x² - 3x + 2 = 0

• Put x = 1 or x = 2

⇢(2)² - 3(2) + 2 = 0

⇢4 - 6 + 2 = 0

⇢-2 + 2 =0

⇢0 = 0

Thus, a = 1 and b = -3⠀⠀⠀⠀⠀⠀⠀⠀