Question

if alpha and beta are the roots of the equation x square - 2 x minus 3 is equal to zero then the equation whose roots are alpha + 2 and beta + 2 iisif alpha and beta are the roots of the equation x square - 2 x minus 3 is equal to zero then the equation whose roots are alpha + 2 and beta + 2 isif alpha and beta are the roots of the equation x square - 2 x minus 3 is equal to zero then the equation whose roots are alpha + 2 and beta + 2 is

Answer 1

Given :- if alpha and beta are the roots of the equation x² - 2x - 3 = 0, then the equation whose roots are (alpha + 2) and (beta + 2) = ?

Solution :-

→ x² - 2x - 3 = 0

→ x² - 3x + x - 3 = 0

→ x(x - 3) + 1(x - 3) = 0

→ (x - 3)(x + 1) = 0

→ x = 3 and (-1) .

So,

• Alpha = 3 .
• Beta = (-1)

then,

• Alpha + 2 = 3 + 2 = 5 .
• Beta = (-1) + 2 = 1 .

So,

• Sum of new roots = 5 + 1 = 6 .
• Product of new roots = 5 * 1 = 5 .

Therefore,

→ Required equation = x² - (sum of roots)x + Product of roots = x² - 6x + 5 = 0 .

Hence, the equation whose roots are (alpha + 2) and (beta + 2) is x² - 6x + 5 = 0 .

Learn more :-

इस एक्स इक्वल टू रूट 3 प्लस वन डिवाइडेड बाय टू फाइंड द वैल्यू ऑफ एक्स क्यूब प्लस टू एक्स स्क्वायर माइनस 8 एक्स प्लस 7

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if a^2+ab+b^2=25

b^2+bc+c^2=49

c^2+ca+a^2=64

Then, find the value of

(a+b+c)² - 100 = ...

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