(i) x2−2x−8
x2−2x−8
=x2−4x+2x−8
=x(x−4)+2(x−4)
=(x+2)(x−4)
Factorize the equation, we got (x+2)(x−4)So, the value of x2−2x−8 is zero when x+2=0,x−4=0, i.e., when x=−2 or x=4.Therefore, the zeros of x2−2x−8 are -2 and 4.Now,⇒Sum of zeroes =−2+4=2=−21=−Coefficient of xCoefficient of x2
⇒Product of zeros =(−2)×(4)=−8 = −81=Constant termCoefficient of x2
(ii) 4s2−4s+1
4s2−4s+1
=4s2−2s−2s+1
=2s(2s−1)−2(2s−1)
=(2s−1)(2s−1)
Factorize the equation, we got (2s−1)(2s−1)So, the value of 4s2−4s+1 is zero when 2s−1=0,2s−1=0, i.e., when s=12 or s=12.Therefore, the zeros of 4s2−4s+1 are 12 and 12.Now,⇒Sum of zeroes = 12+12=1=−−44=−Coefficient of sCoefficient of s2
⇒Product of zeros = 12×12=14=14=Constant termCoefficient of s2
(iii) 6x2−3−7x
=6x2−7x−3
=6x2−9x+2x−3
=3x(2x−3)+1(2x−3)
=(3x+1)(2x−3)
Factorize the equation, we got (3x+1)(2x−3)So, the value of 6x2−3−7x is zero when 3x+1=0,2x−3=0, i.e., when x=−13 or x=32.Therefore, the zeros of 6x2−3−7x are −13 and 32.Now,⇒Sum of zeroes = −13+32=76=−−76=−Coefficient of xCoefficient of x2
⇒Product of zeros = −13×32=−12=−36=−12=Constant termCoefficient of x2
(iv) 4u2+8u
=4u(u+2)
Factorize the equation, we got 4u(u+2)So, the value of 4u2+8u is zero when 4u=0,u+2=0, i.e., when u=0 or u=−2.Therefore, the zeros of 4u2+8u are 0 and −2.Now,⇒Sum of zeroes = 0−2=−2=−84=−2=−Coefficient of uCoefficient of u2
⇒Product of zeros = −0x−2=0=04=0=Constant termCoefficient of u2
(v) t2−15
=t2−(√15)2
So, the value of t2−15 is zero when t+√15=0,t−√15=0, i.e., when t=√15 or t=−√15.Therefore, the zeros of t2−15 are ±√15.Now,⇒Sum of zeroes = √15−√15=0=−01=0=−Coefficient of tCoefficient of t2
⇒Product of zeros = √15×√−15=−15=−151=Constant termCoefficient of t2
(vi) 3x2−x−4
=3x2−x−4
=3x2+3x−4x−4
=3x(x+1)−4(x+1)
=(x+1)(3x−4)
Factorize the equation, we get(x+1)(3x−4)So, the value of 3x2−x−4 is zero when x + 1 = 0, 3x - 4 = 0, i.e., when x = -1 or x = 43.Therefore, the zeros of 3x2−x−4 are -1 and 43.Now,⇒Sum of zeroes = −1+43=13=−−13=−Coefficient of xCoefficient of x2
⇒Product of zeros = −1×43=−43=−43=Constant termCoefficient of x2