 Hello friends, welcome again to another session on problems related to zeros of polynomial The given question says that if x equals to two and x equals to zero are Roots or zeros of the polynomial fx equals to this. So this is if fx given You have to find the values of a and b. So a and b here are unknowns So you have to find the value of a and b What is given given is x equals to two and x equals to zero are the roots So it becomes much easier for us now to solve this Why because by definition if something is a root or a zero of a polynomial Then if you substitute the variable in the polynomial by that value the polynomial itself will reduce to zero. That is what we learned since x equals to two is a Zero or root root of FX Therefore by definition or by knowledge we know f2 that is f of two is Zero correct. So f of what is f of two two times two cube? So replace x by two everywhere wherever you see x you replace it by two so Five times two squared plus a times two plus b is it a and b are unknown and this happens to be zero Let's simplify. So this is eight into two minus five into four twenty plus two a Plus b is zero. That means sixteen minus twenty is minus four. So we get two a Plus b is four Correct. This is equation number one. Let's say now Secondly f of x equals to zero also. Let's say right x equals to zero are roots of the polynomial is also a root of a polynomial so we write since x equals to zero is a zero of FX Therefore f of zero will also be zero Now the zero itself is zero here, right? Zero of the polynomial or the root of the polynomial is zero. So f of zero should be zero This implies what it is. What does it mean? So wherever x is deploy zero zero cubed minus five zero squared Plus a times zero plus b is equal to zero Correct. So what did we eventually get? We will get b is equal to zero Right, so this all will become reduced to zero. So this gives me b equals to zero now b is zero guys Let us say from one if b is zero. What do we see two a plus? zero is four Right b was zero. So a is equal to four upon two which is two Right, therefore we get the values of a as two and b as zero Okay, so in this question, what is the learning? So let's say polynomial is given and some coefficients are unknown, but the zeros are given Then you can find out the unknown coefficients also by using the concept that Zero of a polynomial will reduce the value of the polynomial to zero