Question

If the difference of the roots of x^2 - lambda x + 8 = 0 is 2, the value of lambda is​

Answer 1

GiveN :-

• The difference of roots of quadratic equation is x² - λx + 8 = 0 is 2 .

To FinD :-

• The value of λ .

SolutioN :-

With respect to Standard form of ax² + bx + c = 0 . Sum of zeroes is given by ,

$\boxed{\red{\sf Sum\:of\: zeroes\;=\;\dfrac{-b}{a}=\dfrac{-(coefficient\:of\:x)}{coefficient\:of\:x^2}}}$

Product of zeroes is given by ,

$\boxed{\red{\sf Product\:of\: zeroes\;=\;\dfrac{c}{a}=\dfrac{Constant\:term}{coefficient\:of\:x^2}}}$

If we consider a and ß as its zeroes , then

• a + ß = -b/a = λ /1 = λ
• aß = c/a = 8/1 = 8 .

Also , given that diffrence of roots is 2 . Therefore a - ß = 2

⇒ a - ß = 2

⇒ ( a - ß )² = 2²

⇒ a² + ß² - 2aß = 4

⇒ a² + ß² +2aß - 2aß - 2aß = 4

⇒ ( a + ß )² - 4aß = 4

⇒ λ ² - 4*8 = 4

⇒ λ ² = 32 +4

⇒ λ ² = 36

⇒ λ = √36

⇒ λ = ±6

Hence the value of λ is ± 6 .

$\Large{\boxed{\pink{\sf Value\:of\:\lambda\:=\:\pm 6 }}}$