Question

Q-1) Factorise m(m-3)-n(n-1)

Q-2)If p =2 -a ,prove that a ³+6ap+p³-8 =0

Q-3) If x =2 and x=0 are the zeroes of the polynomials f(x) = 2 x ³-5x²+ax +b ,find the value of a and b ..

Please give correct ans✔️✔️

Answer 1

HELLO DEAR,

---------------------(1) ------------------------

M(M-3) - N(N-1)

=> m²-3m -n²+n

= m²-3m -n²+n

= m²-n²-3m +n

= m²-n²-3m+n + (-m+m)

= (m+n)(m-n) + (m+n) -4m

= (m+n)(m-n+1) -4m

-------------------(2)---------------------

given that:-

p= (2-a)-----------(1)

taking cube both side

we get,

p³= 2³-(a)³ -3 × (2)² a + 3(2) × a²

=> p³ = 8-a³-12a+6a²

=> p³+a³ = 8 -6a(2-a)

=> p³+a³-8 +6ap =0 ----from --(1)

=> a³+6ap+p³-8=0

-------------------------(3)--------------------------

given that:-

x=2 and x=0

----first condition ( x=2)---
$2( {2})^{3} - 5( {2})^{2} + ax + b = 0 \\ \\ = 2 \times 8 - 5 \times 4 + ax + b = 0 \\ \\ = 16 - 20 + ax + b = 0 \\ \\ = 2a + b = 4.......(1)$

----second condition--(x=0)----

$2 ({0})^{3} - 5( {0})^{2} + a(0) + b = 0 \\ \\ = 0 - 0 + 0 + b = 0 \\ \\ b = 0.....(2)$
from--(1) and (2)

$2a+ b = 4 \\ \\ = 2 a = 4 \\ \\ a = \frac{4}{2} \\ \\ a = 2$
a=2 and b=0

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hope it helps u .....................