Question

find a if m and n are the zeroes of the polynomial p(x)=ax^2-35x=12 and m^2+n^2=1

Answer 1

Hi.............

here's your answer................

given,

zeroes of the polynomial 3x²+11x -4  are m and n

⇒ 3(m)² + 11(m) -4 = 0

⇒ 3m²+ 11m -4 = 0

⇒ 3m² +12m -m - 4 = 0

⇒3m( m+ 4) - 1( m + 4)  =0

⇒ (3m - 1) ( m+4) = 0

⇒ (3m - 1) = 0 (or) (m +4 ) = 0

⇒ m = 1/3 or m = -4

if we replace n in x place , we get the same values

Hence , m/n + n/m = 1 + 1 =2

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hope it helps you........................

thanks

Answer 2

Answer:

Since m and n are the zeroes of the polynomial

p(x) = ax² - 35x - 12

So

m + n = 35/a

mn = - 12/a

Now

m² + n² = 1 gives

(m+n)² - 2mn = 1

( 35/a )² - 2 × (-12/a) = 1

a² - 24a - 1225 = 0

a² - (49-25)a - 1225 = 0

a² - 49a + 25a - 1225 = 0

a( a - 49) + 25 (a - 49) = 0

(a - 49) ( a + 25) = 0

Now (a - 49) = 0 gives a = 49

Again ( a + 25) = 0 gives a = - 25

So the required answer is - 25 , 49

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