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Mathematics
Location of roots of quadratic equations
How do you solve ${x^2} + 5x + 7 = 0$ using a quadratic formula?
Mathematics
Location of roots of quadratic equations
If ${x^2} - 6x + 5 = 0$and ${x^2} - 12x + p = 0$ have a common root, then find the value of $p$.

Mathematics
Location of roots of quadratic equations
Solve the following activity: zeroes of the polynomial ${{x}^{2}}-3x+2$ graphically.

Mathematics
Location of roots of quadratic equations
If one root of the quadratic equation \[{{a}_{1}}{{x}^{2}}+{{b}_{1}}x+{{c}_{1}}=0\] is numerically equal but opposite in sign to one root of \[{{a}_{2}}{{x}^{2}}+{{b}_{2}}x+{{c}_{2}}=0\], then prove that the quadratic equation whose roots are the other roots of the both of these equations is $\dfrac{{{x}^{2}}}{\dfrac{{{b}_{1}}}{{{a}_{1}}}+\dfrac{{{b}_{2}}}{{{a}_{2}}}}+x+\dfrac{1}{\dfrac{{{b}_{1}}}{{{c}_{1}}}+\dfrac{{{b}_{2}}}{{{c}_{2}}}}=0$.

Mathematics
Location of roots of quadratic equations
Find the quadratic equation whose sum and product of zeroes are $\dfrac{21}{8}$ and $\dfrac{5}{16}$ respectively.
Mathematics
Location of roots of quadratic equations
Show that the equation ${{x}^{4}}-12{{x}^{2}}+12x-3=0$ has a root between -3 and -4 and another between 2 and 3.

Mathematics
Location of roots of quadratic equations
If $\alpha ,\beta $ are roots of the equation ${{x}^{2}}-6x-2=0$ and we define ${{a}_{n}}={{\alpha }^{n}}-{{\beta }^{n}}$ then find the value of $\dfrac{{{a}_{10}}-2{{a}_{8}}}{2{{a}_{9}}}$

Mathematics
Location of roots of quadratic equations
Consider the quadratic equation $(c-5){{x}^{2}}-2cx+(c-4)=0,c\ne 5$. Let S be the set of all integral values of c for which one root of the equation lies in the interval ( 0, 2 ) and it’s another root lies in the interval ( 2, 3 ). Then the number of elements in S is,
( a ) 11
( b ) 18
( c ) 10
( d ) 12

Mathematics
Location of roots of quadratic equations
For which values of p is \[{{p}^{2}}-5p+6\] negative?
(a) p < 0
(b) 2 < p < 3
(c) p > 3
(d) p < 2
Mathematics
Location of roots of quadratic equations
If the roots of \[a{x^2} + bx + c = 0\] are both negative and \[b < 0\] then
A) \[a < 0,c < 0\]
B) \[a < 0,c > 0\]
C) \[a > 0,c < 0\]
D) \[a > 0,c > 0\]

Mathematics
Location of roots of quadratic equations
If one of the zeros of the quadratic polynomial of the form \[{{x}^{2}}+ax+b\] is negative of the other, then it
(a) has no linear term and the constant term is negative
(b) has no linear term and the constant term is positive
(c) can have a linear term but the constant term is negative
(d) can have a linear term but the constant term is positive.

Mathematics
Location of roots of quadratic equations
Find the zeroes of the polynomial $3{{x}^{2}}-2$ and verify the relationship between the zeroes and coefficients.
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