If a and b zeroes of quadratic polynomial is x2-7x+p. Such a2 + b2 = 29 find the value of p

If a and b zeroes of quadratic polynomial is x2-7x+p. Such a2 + b2 = 2

1.	If a and b zeroes of quadratic polynomial is x2-7x+p. Such a2 + b2 = 29 find the value of p
Answer» Let a and b be the zeroes of the quadratic polynomial x2\xa0-7x+p.By using relationship between coefficient and zeroes of quadratic polynomial we get\xa0sum of zeroes= a+b={tex}{-(-7)\\over 1} = 7{/tex} -----(1)Product of zeroes = a×b ={tex}{p\\over 1}=p{/tex} -----(2)Given a2 + b2\xa0= 29 -----(3)\xa0from eq.(1)a+b=7on squaring both sides(a+b)2 = 72a2\xa0+ 2ab +b2 =49(a2\xa0+b2)+2ab= 49 29+2p =49 [by using eq.(2) ab=p and eq.(3) a2\xa0+ b2 =29] 2p=49-29 2p=20 p={tex}20\\over 2{/tex} p= 10